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Simplifying 6(1 + x) + -8x(-3 + 8x) = 0 (1 * 6 + x * 6) + -8x(-3 + 8x) = 0 (6 + 6x) + -8x(-3 + 8x) = 0 6 + 6x + (-3 * -8x + 8x * -8x) = 0 6 + 6x + (24x + -64x2) = 0 Combine like terms: 6x + 24x = 30x 6 + 30x + -64x2 = 0 Solving 6 + 30x + -64x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 15x + -32x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 15x + -32x2)' equal to zero and attempt to solve: Simplifying 3 + 15x + -32x2 = 0 Solving 3 + 15x + -32x2 = 0 Begin completing the square. Divide all terms by -32 the coefficient of the squared term: Divide each side by '-32'. -0.09375 + -0.46875x + x2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + -0.46875x + 0.09375 + x2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + -0.46875x + x2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + -0.46875x + x2 = 0 + 0.09375 -0.46875x + x2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 -0.46875x + x2 = 0.09375 The x term is -0.46875x. Take half its coefficient (-0.234375). Square it (0.05493164063) and add it to both sides. Add '0.05493164063' to each side of the equation. -0.46875x + 0.05493164063 + x2 = 0.09375 + 0.05493164063 Reorder the terms: 0.05493164063 + -0.46875x + x2 = 0.09375 + 0.05493164063 Combine like terms: 0.09375 + 0.05493164063 = 0.14868164063 0.05493164063 + -0.46875x + x2 = 0.14868164063 Factor a perfect square on the left side: (x + -0.234375)(x + -0.234375) = 0.14868164063 Calculate the square root of the right side: 0.385592584 Break this problem into two subproblems by setting (x + -0.234375) equal to 0.385592584 and -0.385592584.Subproblem 1
x + -0.234375 = 0.385592584 Simplifying x + -0.234375 = 0.385592584 Reorder the terms: -0.234375 + x = 0.385592584 Solving -0.234375 + x = 0.385592584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.234375' to each side of the equation. -0.234375 + 0.234375 + x = 0.385592584 + 0.234375 Combine like terms: -0.234375 + 0.234375 = 0.000000 0.000000 + x = 0.385592584 + 0.234375 x = 0.385592584 + 0.234375 Combine like terms: 0.385592584 + 0.234375 = 0.619967584 x = 0.619967584 Simplifying x = 0.619967584Subproblem 2
x + -0.234375 = -0.385592584 Simplifying x + -0.234375 = -0.385592584 Reorder the terms: -0.234375 + x = -0.385592584 Solving -0.234375 + x = -0.385592584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.234375' to each side of the equation. -0.234375 + 0.234375 + x = -0.385592584 + 0.234375 Combine like terms: -0.234375 + 0.234375 = 0.000000 0.000000 + x = -0.385592584 + 0.234375 x = -0.385592584 + 0.234375 Combine like terms: -0.385592584 + 0.234375 = -0.151217584 x = -0.151217584 Simplifying x = -0.151217584Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.619967584, -0.151217584}Solution
x = {0.619967584, -0.151217584}
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