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Simplifying 15x2 + -7x + -3 = 0 Reorder the terms: -3 + -7x + 15x2 = 0 Solving -3 + -7x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2 + -0.4666666667x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.4666666667x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.4666666667x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.4666666667x + x2 = 0 + 0.2 -0.4666666667x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.4666666667x + x2 = 0.2 The x term is -0.4666666667x. Take half its coefficient (-0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. -0.4666666667x + 0.05444444448 + x2 = 0.2 + 0.05444444448 Reorder the terms: 0.05444444448 + -0.4666666667x + x2 = 0.2 + 0.05444444448 Combine like terms: 0.2 + 0.05444444448 = 0.25444444448 0.05444444448 + -0.4666666667x + x2 = 0.25444444448 Factor a perfect square on the left side: (x + -0.2333333334)(x + -0.2333333334) = 0.25444444448 Calculate the square root of the right side: 0.504424865 Break this problem into two subproblems by setting (x + -0.2333333334) equal to 0.504424865 and -0.504424865.Subproblem 1
x + -0.2333333334 = 0.504424865 Simplifying x + -0.2333333334 = 0.504424865 Reorder the terms: -0.2333333334 + x = 0.504424865 Solving -0.2333333334 + x = 0.504424865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = 0.504424865 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = 0.504424865 + 0.2333333334 x = 0.504424865 + 0.2333333334 Combine like terms: 0.504424865 + 0.2333333334 = 0.7377581984 x = 0.7377581984 Simplifying x = 0.7377581984Subproblem 2
x + -0.2333333334 = -0.504424865 Simplifying x + -0.2333333334 = -0.504424865 Reorder the terms: -0.2333333334 + x = -0.504424865 Solving -0.2333333334 + x = -0.504424865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = -0.504424865 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = -0.504424865 + 0.2333333334 x = -0.504424865 + 0.2333333334 Combine like terms: -0.504424865 + 0.2333333334 = -0.2710915316 x = -0.2710915316 Simplifying x = -0.2710915316Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7377581984, -0.2710915316}
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