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Simplifying 20x2 + 7x + -15 = 0 Reorder the terms: -15 + 7x + 20x2 = 0 Solving -15 + 7x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.75 + 0.35x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.35x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.35x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.35x + x2 = 0 + 0.75 0.35x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.35x + x2 = 0.75 The x term is 0.35x. Take half its coefficient (0.175). Square it (0.030625) and add it to both sides. Add '0.030625' to each side of the equation. 0.35x + 0.030625 + x2 = 0.75 + 0.030625 Reorder the terms: 0.030625 + 0.35x + x2 = 0.75 + 0.030625 Combine like terms: 0.75 + 0.030625 = 0.780625 0.030625 + 0.35x + x2 = 0.780625 Factor a perfect square on the left side: (x + 0.175)(x + 0.175) = 0.780625 Calculate the square root of the right side: 0.883529852 Break this problem into two subproblems by setting (x + 0.175) equal to 0.883529852 and -0.883529852.Subproblem 1
x + 0.175 = 0.883529852 Simplifying x + 0.175 = 0.883529852 Reorder the terms: 0.175 + x = 0.883529852 Solving 0.175 + x = 0.883529852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = 0.883529852 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = 0.883529852 + -0.175 x = 0.883529852 + -0.175 Combine like terms: 0.883529852 + -0.175 = 0.708529852 x = 0.708529852 Simplifying x = 0.708529852Subproblem 2
x + 0.175 = -0.883529852 Simplifying x + 0.175 = -0.883529852 Reorder the terms: 0.175 + x = -0.883529852 Solving 0.175 + x = -0.883529852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = -0.883529852 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = -0.883529852 + -0.175 x = -0.883529852 + -0.175 Combine like terms: -0.883529852 + -0.175 = -1.058529852 x = -1.058529852 Simplifying x = -1.058529852Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.708529852, -1.058529852}
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