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Simplifying 4(x + -6) = 8x(4x + 24) Reorder the terms: 4(-6 + x) = 8x(4x + 24) (-6 * 4 + x * 4) = 8x(4x + 24) (-24 + 4x) = 8x(4x + 24) Reorder the terms: -24 + 4x = 8x(24 + 4x) -24 + 4x = (24 * 8x + 4x * 8x) -24 + 4x = (192x + 32x2) Solving -24 + 4x = 192x + 32x2 Solving for variable 'x'. Combine like terms: 4x + -192x = -188x -24 + -188x + -32x2 = 192x + 32x2 + -192x + -32x2 Reorder the terms: -24 + -188x + -32x2 = 192x + -192x + 32x2 + -32x2 Combine like terms: 192x + -192x = 0 -24 + -188x + -32x2 = 0 + 32x2 + -32x2 -24 + -188x + -32x2 = 32x2 + -32x2 Combine like terms: 32x2 + -32x2 = 0 -24 + -188x + -32x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(6 + 47x + 8x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(6 + 47x + 8x2)' equal to zero and attempt to solve: Simplifying 6 + 47x + 8x2 = 0 Solving 6 + 47x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.75 + 5.875x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 5.875x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 5.875x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 5.875x + x2 = 0 + -0.75 5.875x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 5.875x + x2 = -0.75 The x term is 5.875x. Take half its coefficient (2.9375). Square it (8.62890625) and add it to both sides. Add '8.62890625' to each side of the equation. 5.875x + 8.62890625 + x2 = -0.75 + 8.62890625 Reorder the terms: 8.62890625 + 5.875x + x2 = -0.75 + 8.62890625 Combine like terms: -0.75 + 8.62890625 = 7.87890625 8.62890625 + 5.875x + x2 = 7.87890625 Factor a perfect square on the left side: (x + 2.9375)(x + 2.9375) = 7.87890625 Calculate the square root of the right side: 2.806938947 Break this problem into two subproblems by setting (x + 2.9375) equal to 2.806938947 and -2.806938947.Subproblem 1
x + 2.9375 = 2.806938947 Simplifying x + 2.9375 = 2.806938947 Reorder the terms: 2.9375 + x = 2.806938947 Solving 2.9375 + x = 2.806938947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.9375' to each side of the equation. 2.9375 + -2.9375 + x = 2.806938947 + -2.9375 Combine like terms: 2.9375 + -2.9375 = 0.0000 0.0000 + x = 2.806938947 + -2.9375 x = 2.806938947 + -2.9375 Combine like terms: 2.806938947 + -2.9375 = -0.130561053 x = -0.130561053 Simplifying x = -0.130561053Subproblem 2
x + 2.9375 = -2.806938947 Simplifying x + 2.9375 = -2.806938947 Reorder the terms: 2.9375 + x = -2.806938947 Solving 2.9375 + x = -2.806938947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.9375' to each side of the equation. 2.9375 + -2.9375 + x = -2.806938947 + -2.9375 Combine like terms: 2.9375 + -2.9375 = 0.0000 0.0000 + x = -2.806938947 + -2.9375 x = -2.806938947 + -2.9375 Combine like terms: -2.806938947 + -2.9375 = -5.744438947 x = -5.744438947 Simplifying x = -5.744438947Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.130561053, -5.744438947}Solution
x = {-0.130561053, -5.744438947}
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