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Simplifying 3x = 10x2 + -2 Reorder the terms: 3x = -2 + 10x2 Solving 3x = -2 + 10x2 Solving for variable 'x'. Reorder the terms: 2 + 3x + -10x2 = -2 + 10x2 + 2 + -10x2 Reorder the terms: 2 + 3x + -10x2 = -2 + 2 + 10x2 + -10x2 Combine like terms: -2 + 2 = 0 2 + 3x + -10x2 = 0 + 10x2 + -10x2 2 + 3x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 2 + 3x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.2 + -0.3x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.3x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.3x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.3x + x2 = 0 + 0.2 -0.3x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.3x + x2 = 0.2 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 0.2 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 0.2 + 0.0225 Combine like terms: 0.2 + 0.0225 = 0.2225 0.0225 + -0.3x + x2 = 0.2225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 0.2225 Calculate the square root of the right side: 0.471699057 Break this problem into two subproblems by setting (x + -0.15) equal to 0.471699057 and -0.471699057.Subproblem 1
x + -0.15 = 0.471699057 Simplifying x + -0.15 = 0.471699057 Reorder the terms: -0.15 + x = 0.471699057 Solving -0.15 + x = 0.471699057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 0.471699057 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.471699057 + 0.15 x = 0.471699057 + 0.15 Combine like terms: 0.471699057 + 0.15 = 0.621699057 x = 0.621699057 Simplifying x = 0.621699057Subproblem 2
x + -0.15 = -0.471699057 Simplifying x + -0.15 = -0.471699057 Reorder the terms: -0.15 + x = -0.471699057 Solving -0.15 + x = -0.471699057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -0.471699057 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.471699057 + 0.15 x = -0.471699057 + 0.15 Combine like terms: -0.471699057 + 0.15 = -0.321699057 x = -0.321699057 Simplifying x = -0.321699057Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.621699057, -0.321699057}
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