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Simplifying 5x2 + 2(2x + -9) = 0 Reorder the terms: 5x2 + 2(-9 + 2x) = 0 5x2 + (-9 * 2 + 2x * 2) = 0 5x2 + (-18 + 4x) = 0 Reorder the terms: -18 + 4x + 5x2 = 0 Solving -18 + 4x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + 0.8x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 0.8x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 0.8x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 0.8x + x2 = 0 + 3.6 0.8x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 0.8x + x2 = 3.6 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 3.6 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 3.6 + 0.16 Combine like terms: 3.6 + 0.16 = 3.76 0.16 + 0.8x + x2 = 3.76 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 3.76 Calculate the square root of the right side: 1.939071943 Break this problem into two subproblems by setting (x + 0.4) equal to 1.939071943 and -1.939071943.Subproblem 1
x + 0.4 = 1.939071943 Simplifying x + 0.4 = 1.939071943 Reorder the terms: 0.4 + x = 1.939071943 Solving 0.4 + x = 1.939071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.939071943 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.939071943 + -0.4 x = 1.939071943 + -0.4 Combine like terms: 1.939071943 + -0.4 = 1.539071943 x = 1.539071943 Simplifying x = 1.539071943Subproblem 2
x + 0.4 = -1.939071943 Simplifying x + 0.4 = -1.939071943 Reorder the terms: 0.4 + x = -1.939071943 Solving 0.4 + x = -1.939071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.939071943 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.939071943 + -0.4 x = -1.939071943 + -0.4 Combine like terms: -1.939071943 + -0.4 = -2.339071943 x = -2.339071943 Simplifying x = -2.339071943Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.539071943, -2.339071943}
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