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Simplifying (8x + 3)(8x + 3) = 63 Reorder the terms: (3 + 8x)(8x + 3) = 63 Reorder the terms: (3 + 8x)(3 + 8x) = 63 Multiply (3 + 8x) * (3 + 8x) (3(3 + 8x) + 8x * (3 + 8x)) = 63 ((3 * 3 + 8x * 3) + 8x * (3 + 8x)) = 63 ((9 + 24x) + 8x * (3 + 8x)) = 63 (9 + 24x + (3 * 8x + 8x * 8x)) = 63 (9 + 24x + (24x + 64x2)) = 63 Combine like terms: 24x + 24x = 48x (9 + 48x + 64x2) = 63 Solving 9 + 48x + 64x2 = 63 Solving for variable 'x'. Reorder the terms: 9 + -63 + 48x + 64x2 = 63 + -63 Combine like terms: 9 + -63 = -54 -54 + 48x + 64x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -54 + 48x + 64x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 24x + 32x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + 24x + 32x2)' equal to zero and attempt to solve: Simplifying -27 + 24x + 32x2 = 0 Solving -27 + 24x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.84375 + 0.75x + x2 = 0 Move the constant term to the right: Add '0.84375' to each side of the equation. -0.84375 + 0.75x + 0.84375 + x2 = 0 + 0.84375 Reorder the terms: -0.84375 + 0.84375 + 0.75x + x2 = 0 + 0.84375 Combine like terms: -0.84375 + 0.84375 = 0.00000 0.00000 + 0.75x + x2 = 0 + 0.84375 0.75x + x2 = 0 + 0.84375 Combine like terms: 0 + 0.84375 = 0.84375 0.75x + x2 = 0.84375 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 0.84375 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.84375 + 0.140625 Combine like terms: 0.84375 + 0.140625 = 0.984375 0.140625 + 0.75x + x2 = 0.984375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.984375 Calculate the square root of the right side: 0.992156742 Break this problem into two subproblems by setting (x + 0.375) equal to 0.992156742 and -0.992156742.Subproblem 1
x + 0.375 = 0.992156742 Simplifying x + 0.375 = 0.992156742 Reorder the terms: 0.375 + x = 0.992156742 Solving 0.375 + x = 0.992156742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.992156742 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.992156742 + -0.375 x = 0.992156742 + -0.375 Combine like terms: 0.992156742 + -0.375 = 0.617156742 x = 0.617156742 Simplifying x = 0.617156742Subproblem 2
x + 0.375 = -0.992156742 Simplifying x + 0.375 = -0.992156742 Reorder the terms: 0.375 + x = -0.992156742 Solving 0.375 + x = -0.992156742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -0.992156742 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.992156742 + -0.375 x = -0.992156742 + -0.375 Combine like terms: -0.992156742 + -0.375 = -1.367156742 x = -1.367156742 Simplifying x = -1.367156742Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.617156742, -1.367156742}Solution
x = {0.617156742, -1.367156742}
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