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Simplifying 10(x * x + 3) = -2x * -2x + x + 12x * 12x Multiply x * x 10(x2 + 3) = -2x * -2x + x + 12x * 12x Reorder the terms: 10(3 + x2) = -2x * -2x + x + 12x * 12x (3 * 10 + x2 * 10) = -2x * -2x + x + 12x * 12x (30 + 10x2) = -2x * -2x + x + 12x * 12x Reorder the terms for easier multiplication: 30 + 10x2 = -2 * -2x * x + x + 12x * 12x Multiply -2 * -2 30 + 10x2 = 4x * x + x + 12x * 12x Multiply x * x 30 + 10x2 = 4x2 + x + 12x * 12x Reorder the terms for easier multiplication: 30 + 10x2 = 4x2 + x + 12 * 12x * x Multiply 12 * 12 30 + 10x2 = 4x2 + x + 144x * x Multiply x * x 30 + 10x2 = 4x2 + x + 144x2 Reorder the terms: 30 + 10x2 = x + 4x2 + 144x2 Combine like terms: 4x2 + 144x2 = 148x2 30 + 10x2 = x + 148x2 Solving 30 + 10x2 = x + 148x2 Solving for variable 'x'. Reorder the terms: 30 + -1x + 10x2 + -148x2 = x + 148x2 + -1x + -148x2 Combine like terms: 10x2 + -148x2 = -138x2 30 + -1x + -138x2 = x + 148x2 + -1x + -148x2 Reorder the terms: 30 + -1x + -138x2 = x + -1x + 148x2 + -148x2 Combine like terms: x + -1x = 0 30 + -1x + -138x2 = 0 + 148x2 + -148x2 30 + -1x + -138x2 = 148x2 + -148x2 Combine like terms: 148x2 + -148x2 = 0 30 + -1x + -138x2 = 0 Begin completing the square. Divide all terms by -138 the coefficient of the squared term: Divide each side by '-138'. -0.2173913043 + 0.007246376812x + x2 = 0 Move the constant term to the right: Add '0.2173913043' to each side of the equation. -0.2173913043 + 0.007246376812x + 0.2173913043 + x2 = 0 + 0.2173913043 Reorder the terms: -0.2173913043 + 0.2173913043 + 0.007246376812x + x2 = 0 + 0.2173913043 Combine like terms: -0.2173913043 + 0.2173913043 = 0.0000000000 0.0000000000 + 0.007246376812x + x2 = 0 + 0.2173913043 0.007246376812x + x2 = 0 + 0.2173913043 Combine like terms: 0 + 0.2173913043 = 0.2173913043 0.007246376812x + x2 = 0.2173913043 The x term is 0.007246376812x. Take half its coefficient (0.003623188406). Square it (0.00001312749423) and add it to both sides. Add '0.00001312749423' to each side of the equation. 0.007246376812x + 0.00001312749423 + x2 = 0.2173913043 + 0.00001312749423 Reorder the terms: 0.00001312749423 + 0.007246376812x + x2 = 0.2173913043 + 0.00001312749423 Combine like terms: 0.2173913043 + 0.00001312749423 = 0.21740443179423 0.00001312749423 + 0.007246376812x + x2 = 0.21740443179423 Factor a perfect square on the left side: (x + 0.003623188406)(x + 0.003623188406) = 0.21740443179423 Calculate the square root of the right side: 0.466266482 Break this problem into two subproblems by setting (x + 0.003623188406) equal to 0.466266482 and -0.466266482.Subproblem 1
x + 0.003623188406 = 0.466266482 Simplifying x + 0.003623188406 = 0.466266482 Reorder the terms: 0.003623188406 + x = 0.466266482 Solving 0.003623188406 + x = 0.466266482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.003623188406' to each side of the equation. 0.003623188406 + -0.003623188406 + x = 0.466266482 + -0.003623188406 Combine like terms: 0.003623188406 + -0.003623188406 = 0.000000000000 0.000000000000 + x = 0.466266482 + -0.003623188406 x = 0.466266482 + -0.003623188406 Combine like terms: 0.466266482 + -0.003623188406 = 0.462643293594 x = 0.462643293594 Simplifying x = 0.462643293594Subproblem 2
x + 0.003623188406 = -0.466266482 Simplifying x + 0.003623188406 = -0.466266482 Reorder the terms: 0.003623188406 + x = -0.466266482 Solving 0.003623188406 + x = -0.466266482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.003623188406' to each side of the equation. 0.003623188406 + -0.003623188406 + x = -0.466266482 + -0.003623188406 Combine like terms: 0.003623188406 + -0.003623188406 = 0.000000000000 0.000000000000 + x = -0.466266482 + -0.003623188406 x = -0.466266482 + -0.003623188406 Combine like terms: -0.466266482 + -0.003623188406 = -0.469889670406 x = -0.469889670406 Simplifying x = -0.469889670406Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.462643293594, -0.469889670406}
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