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Simplifying 566(6 + x) * x + 5 = 10 Reorder the terms for easier multiplication: 566x(6 + x) + 5 = 10 (6 * 566x + x * 566x) + 5 = 10 (3396x + 566x2) + 5 = 10 Reorder the terms: 5 + 3396x + 566x2 = 10 Solving 5 + 3396x + 566x2 = 10 Solving for variable 'x'. Reorder the terms: 5 + -10 + 3396x + 566x2 = 10 + -10 Combine like terms: 5 + -10 = -5 -5 + 3396x + 566x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -5 + 3396x + 566x2 = 0 Begin completing the square. Divide all terms by 566 the coefficient of the squared term: Divide each side by '566'. -0.008833922261 + 6x + x2 = 0 Move the constant term to the right: Add '0.008833922261' to each side of the equation. -0.008833922261 + 6x + 0.008833922261 + x2 = 0 + 0.008833922261 Reorder the terms: -0.008833922261 + 0.008833922261 + 6x + x2 = 0 + 0.008833922261 Combine like terms: -0.008833922261 + 0.008833922261 = 0.000000000000 0.000000000000 + 6x + x2 = 0 + 0.008833922261 6x + x2 = 0 + 0.008833922261 Combine like terms: 0 + 0.008833922261 = 0.008833922261 6x + x2 = 0.008833922261 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 0.008833922261 + 9 Reorder the terms: 9 + 6x + x2 = 0.008833922261 + 9 Combine like terms: 0.008833922261 + 9 = 9.008833922261 9 + 6x + x2 = 9.008833922261 Factor a perfect square on the left side: (x + 3)(x + 3) = 9.008833922261 Calculate the square root of the right side: 3.001471959 Break this problem into two subproblems by setting (x + 3) equal to 3.001471959 and -3.001471959.Subproblem 1
x + 3 = 3.001471959 Simplifying x + 3 = 3.001471959 Reorder the terms: 3 + x = 3.001471959 Solving 3 + x = 3.001471959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.001471959 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.001471959 + -3 x = 3.001471959 + -3 Combine like terms: 3.001471959 + -3 = 0.001471959 x = 0.001471959 Simplifying x = 0.001471959Subproblem 2
x + 3 = -3.001471959 Simplifying x + 3 = -3.001471959 Reorder the terms: 3 + x = -3.001471959 Solving 3 + x = -3.001471959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.001471959 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.001471959 + -3 x = -3.001471959 + -3 Combine like terms: -3.001471959 + -3 = -6.001471959 x = -6.001471959 Simplifying x = -6.001471959Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.001471959, -6.001471959}
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