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Simplifying 8x(2x + 3) = x + 1 Reorder the terms: 8x(3 + 2x) = x + 1 (3 * 8x + 2x * 8x) = x + 1 (24x + 16x2) = x + 1 Reorder the terms: 24x + 16x2 = 1 + x Solving 24x + 16x2 = 1 + x Solving for variable 'x'. Reorder the terms: -1 + 24x + -1x + 16x2 = 1 + x + -1 + -1x Combine like terms: 24x + -1x = 23x -1 + 23x + 16x2 = 1 + x + -1 + -1x Reorder the terms: -1 + 23x + 16x2 = 1 + -1 + x + -1x Combine like terms: 1 + -1 = 0 -1 + 23x + 16x2 = 0 + x + -1x -1 + 23x + 16x2 = x + -1x Combine like terms: x + -1x = 0 -1 + 23x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + 1.4375x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 1.4375x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 1.4375x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 1.4375x + x2 = 0 + 0.0625 1.4375x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 1.4375x + x2 = 0.0625 The x term is 1.4375x. Take half its coefficient (0.71875). Square it (0.5166015625) and add it to both sides. Add '0.5166015625' to each side of the equation. 1.4375x + 0.5166015625 + x2 = 0.0625 + 0.5166015625 Reorder the terms: 0.5166015625 + 1.4375x + x2 = 0.0625 + 0.5166015625 Combine like terms: 0.0625 + 0.5166015625 = 0.5791015625 0.5166015625 + 1.4375x + x2 = 0.5791015625 Factor a perfect square on the left side: (x + 0.71875)(x + 0.71875) = 0.5791015625 Calculate the square root of the right side: 0.760987229 Break this problem into two subproblems by setting (x + 0.71875) equal to 0.760987229 and -0.760987229.Subproblem 1
x + 0.71875 = 0.760987229 Simplifying x + 0.71875 = 0.760987229 Reorder the terms: 0.71875 + x = 0.760987229 Solving 0.71875 + x = 0.760987229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + x = 0.760987229 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + x = 0.760987229 + -0.71875 x = 0.760987229 + -0.71875 Combine like terms: 0.760987229 + -0.71875 = 0.042237229 x = 0.042237229 Simplifying x = 0.042237229Subproblem 2
x + 0.71875 = -0.760987229 Simplifying x + 0.71875 = -0.760987229 Reorder the terms: 0.71875 + x = -0.760987229 Solving 0.71875 + x = -0.760987229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + x = -0.760987229 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + x = -0.760987229 + -0.71875 x = -0.760987229 + -0.71875 Combine like terms: -0.760987229 + -0.71875 = -1.479737229 x = -1.479737229 Simplifying x = -1.479737229Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.042237229, -1.479737229}
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