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Simplifying 15x2 + 6x + -12 = 27 Reorder the terms: -12 + 6x + 15x2 = 27 Solving -12 + 6x + 15x2 = 27 Solving for variable 'x'. Reorder the terms: -12 + -27 + 6x + 15x2 = 27 + -27 Combine like terms: -12 + -27 = -39 -39 + 6x + 15x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -39 + 6x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + 2x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + 2x + 5x2)' equal to zero and attempt to solve: Simplifying -13 + 2x + 5x2 = 0 Solving -13 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + 0.4x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 0.4x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 0.4x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 0.4x + x2 = 0 + 2.6 0.4x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 0.4x + x2 = 2.6 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 2.6 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 2.6 + 0.04 Combine like terms: 2.6 + 0.04 = 2.64 0.04 + 0.4x + x2 = 2.64 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 2.64 Calculate the square root of the right side: 1.624807681 Break this problem into two subproblems by setting (x + 0.2) equal to 1.624807681 and -1.624807681.Subproblem 1
x + 0.2 = 1.624807681 Simplifying x + 0.2 = 1.624807681 Reorder the terms: 0.2 + x = 1.624807681 Solving 0.2 + x = 1.624807681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.624807681 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.624807681 + -0.2 x = 1.624807681 + -0.2 Combine like terms: 1.624807681 + -0.2 = 1.424807681 x = 1.424807681 Simplifying x = 1.424807681Subproblem 2
x + 0.2 = -1.624807681 Simplifying x + 0.2 = -1.624807681 Reorder the terms: 0.2 + x = -1.624807681 Solving 0.2 + x = -1.624807681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.624807681 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.624807681 + -0.2 x = -1.624807681 + -0.2 Combine like terms: -1.624807681 + -0.2 = -1.824807681 x = -1.824807681 Simplifying x = -1.824807681Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.424807681, -1.824807681}Solution
x = {1.424807681, -1.824807681}
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