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Simplifying -4x2 + 8x = -6 Reorder the terms: 8x + -4x2 = -6 Solving 8x + -4x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + 8x + -4x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 8x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 4x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 4x + -2x2)' equal to zero and attempt to solve: Simplifying 3 + 4x + -2x2 = 0 Solving 3 + 4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1.5 + -2x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2x + x2 = 0 + 1.5 -2x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2x + x2 = 1.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.5 + 1 Reorder the terms: 1 + -2x + x2 = 1.5 + 1 Combine like terms: 1.5 + 1 = 2.5 1 + -2x + x2 = 2.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (x + -1) equal to 1.58113883 and -1.58113883.Subproblem 1
x + -1 = 1.58113883 Simplifying x + -1 = 1.58113883 Reorder the terms: -1 + x = 1.58113883 Solving -1 + x = 1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.58113883 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.58113883 + 1 x = 1.58113883 + 1 Combine like terms: 1.58113883 + 1 = 2.58113883 x = 2.58113883 Simplifying x = 2.58113883Subproblem 2
x + -1 = -1.58113883 Simplifying x + -1 = -1.58113883 Reorder the terms: -1 + x = -1.58113883 Solving -1 + x = -1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.58113883 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.58113883 + 1 x = -1.58113883 + 1 Combine like terms: -1.58113883 + 1 = -0.58113883 x = -0.58113883 Simplifying x = -0.58113883Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.58113883, -0.58113883}Solution
x = {2.58113883, -0.58113883}
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