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Simplifying 10x2 + 12x + -116 = 0 Reorder the terms: -116 + 12x + 10x2 = 0 Solving -116 + 12x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-58 + 6x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-58 + 6x + 5x2)' equal to zero and attempt to solve: Simplifying -58 + 6x + 5x2 = 0 Solving -58 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11.6 + 1.2x + x2 = 0 Move the constant term to the right: Add '11.6' to each side of the equation. -11.6 + 1.2x + 11.6 + x2 = 0 + 11.6 Reorder the terms: -11.6 + 11.6 + 1.2x + x2 = 0 + 11.6 Combine like terms: -11.6 + 11.6 = 0.0 0.0 + 1.2x + x2 = 0 + 11.6 1.2x + x2 = 0 + 11.6 Combine like terms: 0 + 11.6 = 11.6 1.2x + x2 = 11.6 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 = 11.6 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 11.6 + 0.36 Combine like terms: 11.6 + 0.36 = 11.96 0.36 + 1.2x + x2 = 11.96 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 11.96 Calculate the square root of the right side: 3.458323293 Break this problem into two subproblems by setting (x + 0.6) equal to 3.458323293 and -3.458323293.Subproblem 1
x + 0.6 = 3.458323293 Simplifying x + 0.6 = 3.458323293 Reorder the terms: 0.6 + x = 3.458323293 Solving 0.6 + x = 3.458323293 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 = 3.458323293 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 3.458323293 + -0.6 x = 3.458323293 + -0.6 Combine like terms: 3.458323293 + -0.6 = 2.858323293 x = 2.858323293 Simplifying x = 2.858323293Subproblem 2
x + 0.6 = -3.458323293 Simplifying x + 0.6 = -3.458323293 Reorder the terms: 0.6 + x = -3.458323293 Solving 0.6 + x = -3.458323293 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 = -3.458323293 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -3.458323293 + -0.6 x = -3.458323293 + -0.6 Combine like terms: -3.458323293 + -0.6 = -4.058323293 x = -4.058323293 Simplifying x = -4.058323293Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.858323293, -4.058323293}Solution
x = {2.858323293, -4.058323293}
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