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Simplifying 10x2 + 3x + 3 = 5 Reorder the terms: 3 + 3x + 10x2 = 5 Solving 3 + 3x + 10x2 = 5 Solving for variable 'x'. Reorder the terms: 3 + -5 + 3x + 10x2 = 5 + -5 Combine like terms: 3 + -5 = -2 -2 + 3x + 10x2 = 5 + -5 Combine like terms: 5 + -5 = 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 = 0.321699057 x = 0.321699057 Simplifying x = 0.321699057Subproblem 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 = -0.621699057 x = -0.621699057 Simplifying x = -0.621699057Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.321699057, -0.621699057}
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