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Simplifying 5x(4 + 6x) + -3 = 0 (4 * 5x + 6x * 5x) + -3 = 0 (20x + 30x2) + -3 = 0 Reorder the terms: -3 + 20x + 30x2 = 0 Solving -3 + 20x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.1 + 0.6666666667x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.6666666667x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.6666666667x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.6666666667x + x2 = 0.0 + 0.1 0.6666666667x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 0.6666666667x + x2 = 0.1 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.1 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.1 + 0.1111111112 Combine like terms: 0.1 + 0.1111111112 = 0.2111111112 0.1111111112 + 0.6666666667x + x2 = 0.2111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.2111111112 Calculate the square root of the right side: 0.459468292 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.459468292 and -0.459468292.Subproblem 1
x + 0.3333333334 = 0.459468292 Simplifying x + 0.3333333334 = 0.459468292 Reorder the terms: 0.3333333334 + x = 0.459468292 Solving 0.3333333334 + x = 0.459468292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.459468292 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.459468292 + -0.3333333334 x = 0.459468292 + -0.3333333334 Combine like terms: 0.459468292 + -0.3333333334 = 0.1261349586 x = 0.1261349586 Simplifying x = 0.1261349586Subproblem 2
x + 0.3333333334 = -0.459468292 Simplifying x + 0.3333333334 = -0.459468292 Reorder the terms: 0.3333333334 + x = -0.459468292 Solving 0.3333333334 + x = -0.459468292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.459468292 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.459468292 + -0.3333333334 x = -0.459468292 + -0.3333333334 Combine like terms: -0.459468292 + -0.3333333334 = -0.7928016254 x = -0.7928016254 Simplifying x = -0.7928016254Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1261349586, -0.7928016254}
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