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Simplifying 5x(3x + 3) = x + 6 Reorder the terms: 5x(3 + 3x) = x + 6 (3 * 5x + 3x * 5x) = x + 6 (15x + 15x2) = x + 6 Reorder the terms: 15x + 15x2 = 6 + x Solving 15x + 15x2 = 6 + x Solving for variable 'x'. Reorder the terms: -6 + 15x + -1x + 15x2 = 6 + x + -6 + -1x Combine like terms: 15x + -1x = 14x -6 + 14x + 15x2 = 6 + x + -6 + -1x Reorder the terms: -6 + 14x + 15x2 = 6 + -6 + x + -1x Combine like terms: 6 + -6 = 0 -6 + 14x + 15x2 = 0 + x + -1x -6 + 14x + 15x2 = x + -1x Combine like terms: x + -1x = 0 -6 + 14x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.4 + 0.9333333333x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.9333333333x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.9333333333x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.9333333333x + x2 = 0 + 0.4 0.9333333333x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.9333333333x + x2 = 0.4 The x term is 0.9333333333x. Take half its coefficient (0.4666666667). Square it (0.2177777778) and add it to both sides. Add '0.2177777778' to each side of the equation. 0.9333333333x + 0.2177777778 + x2 = 0.4 + 0.2177777778 Reorder the terms: 0.2177777778 + 0.9333333333x + x2 = 0.4 + 0.2177777778 Combine like terms: 0.4 + 0.2177777778 = 0.6177777778 0.2177777778 + 0.9333333333x + x2 = 0.6177777778 Factor a perfect square on the left side: (x + 0.4666666667)(x + 0.4666666667) = 0.6177777778 Calculate the square root of the right side: 0.785988408 Break this problem into two subproblems by setting (x + 0.4666666667) equal to 0.785988408 and -0.785988408.Subproblem 1
x + 0.4666666667 = 0.785988408 Simplifying x + 0.4666666667 = 0.785988408 Reorder the terms: 0.4666666667 + x = 0.785988408 Solving 0.4666666667 + x = 0.785988408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = 0.785988408 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = 0.785988408 + -0.4666666667 x = 0.785988408 + -0.4666666667 Combine like terms: 0.785988408 + -0.4666666667 = 0.3193217413 x = 0.3193217413 Simplifying x = 0.3193217413Subproblem 2
x + 0.4666666667 = -0.785988408 Simplifying x + 0.4666666667 = -0.785988408 Reorder the terms: 0.4666666667 + x = -0.785988408 Solving 0.4666666667 + x = -0.785988408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = -0.785988408 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = -0.785988408 + -0.4666666667 x = -0.785988408 + -0.4666666667 Combine like terms: -0.785988408 + -0.4666666667 = -1.2526550747 x = -1.2526550747 Simplifying x = -1.2526550747Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3193217413, -1.2526550747}
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