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Simplifying 10x2 + -16x = 12 Reorder the terms: -16x + 10x2 = 12 Solving -16x + 10x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -16x + 10x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -16x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -8x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -8x + 5x2)' equal to zero and attempt to solve: Simplifying -6 + -8x + 5x2 = 0 Solving -6 + -8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -1.6x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -1.6x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -1.6x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -1.6x + x2 = 0 + 1.2 -1.6x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -1.6x + x2 = 1.2 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 1.2 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 1.2 + 0.64 Combine like terms: 1.2 + 0.64 = 1.84 0.64 + -1.6x + x2 = 1.84 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x + -0.8) equal to 1.356465997 and -1.356465997.Subproblem 1
x + -0.8 = 1.356465997 Simplifying x + -0.8 = 1.356465997 Reorder the terms: -0.8 + x = 1.356465997 Solving -0.8 + x = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.356465997 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.356465997 + 0.8 x = 1.356465997 + 0.8 Combine like terms: 1.356465997 + 0.8 = 2.156465997 x = 2.156465997 Simplifying x = 2.156465997Subproblem 2
x + -0.8 = -1.356465997 Simplifying x + -0.8 = -1.356465997 Reorder the terms: -0.8 + x = -1.356465997 Solving -0.8 + x = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.356465997 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.356465997 + 0.8 x = -1.356465997 + 0.8 Combine like terms: -1.356465997 + 0.8 = -0.556465997 x = -0.556465997 Simplifying x = -0.556465997Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.156465997, -0.556465997}Solution
x = {2.156465997, -0.556465997}
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