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Simplifying 10x2 + -12 = -12x Reorder the terms: -12 + 10x2 = -12x Solving -12 + 10x2 = -12x Solving for variable 'x'. Reorder the terms: -12 + 12x + 10x2 = -12x + 12x Combine like terms: -12x + 12x = 0 -12 + 12x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 6x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 6x + 5x2)' equal to zero and attempt to solve: Simplifying -6 + 6x + 5x2 = 0 Solving -6 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 1.2x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 1.2x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 1.2x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 1.2x + x2 = 0 + 1.2 1.2x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 1.2x + x2 = 1.2 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 1.2 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 1.2 + 0.36 Combine like terms: 1.2 + 0.36 = 1.56 0.36 + 1.2x + x2 = 1.56 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (x + 0.6) equal to 1.2489996 and -1.2489996.Subproblem 1
x + 0.6 = 1.2489996 Simplifying x + 0.6 = 1.2489996 Reorder the terms: 0.6 + x = 1.2489996 Solving 0.6 + x = 1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 1.2489996 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 1.2489996 + -0.6 x = 1.2489996 + -0.6 Combine like terms: 1.2489996 + -0.6 = 0.6489996 x = 0.6489996 Simplifying x = 0.6489996Subproblem 2
x + 0.6 = -1.2489996 Simplifying x + 0.6 = -1.2489996 Reorder the terms: 0.6 + x = -1.2489996 Solving 0.6 + x = -1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -1.2489996 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -1.2489996 + -0.6 x = -1.2489996 + -0.6 Combine like terms: -1.2489996 + -0.6 = -1.8489996 x = -1.8489996 Simplifying x = -1.8489996Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6489996, -1.8489996}Solution
x = {0.6489996, -1.8489996}
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