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Simplifying x(4x + -6) + -9 = 6 Reorder the terms: x(-6 + 4x) + -9 = 6 (-6 * x + 4x * x) + -9 = 6 (-6x + 4x2) + -9 = 6 Reorder the terms: -9 + -6x + 4x2 = 6 Solving -9 + -6x + 4x2 = 6 Solving for variable 'x'. Reorder the terms: -9 + -6 + -6x + 4x2 = 6 + -6 Combine like terms: -9 + -6 = -15 -15 + -6x + 4x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -15 + -6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -1.5x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -1.5x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -1.5x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -1.5x + x2 = 0 + 3.75 -1.5x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -1.5x + x2 = 3.75 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 3.75 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 3.75 + 0.5625 Combine like terms: 3.75 + 0.5625 = 4.3125 0.5625 + -1.5x + x2 = 4.3125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (x + -0.75) equal to 2.076655966 and -2.076655966.Subproblem 1
x + -0.75 = 2.076655966 Simplifying x + -0.75 = 2.076655966 Reorder the terms: -0.75 + x = 2.076655966 Solving -0.75 + x = 2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.076655966 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.076655966 + 0.75 x = 2.076655966 + 0.75 Combine like terms: 2.076655966 + 0.75 = 2.826655966 x = 2.826655966 Simplifying x = 2.826655966Subproblem 2
x + -0.75 = -2.076655966 Simplifying x + -0.75 = -2.076655966 Reorder the terms: -0.75 + x = -2.076655966 Solving -0.75 + x = -2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.076655966 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.076655966 + 0.75 x = -2.076655966 + 0.75 Combine like terms: -2.076655966 + 0.75 = -1.326655966 x = -1.326655966 Simplifying x = -1.326655966Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.826655966, -1.326655966}
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