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Simplifying 28x2 + -43x + -15 = 0 Reorder the terms: -15 + -43x + 28x2 = 0 Solving -15 + -43x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.5357142857 + -1.535714286x + x2 = 0 Move the constant term to the right: Add '0.5357142857' to each side of the equation. -0.5357142857 + -1.535714286x + 0.5357142857 + x2 = 0 + 0.5357142857 Reorder the terms: -0.5357142857 + 0.5357142857 + -1.535714286x + x2 = 0 + 0.5357142857 Combine like terms: -0.5357142857 + 0.5357142857 = 0.0000000000 0.0000000000 + -1.535714286x + x2 = 0 + 0.5357142857 -1.535714286x + x2 = 0 + 0.5357142857 Combine like terms: 0 + 0.5357142857 = 0.5357142857 -1.535714286x + x2 = 0.5357142857 The x term is -1.535714286x. Take half its coefficient (-0.767857143). Square it (0.5896045921) and add it to both sides. Add '0.5896045921' to each side of the equation. -1.535714286x + 0.5896045921 + x2 = 0.5357142857 + 0.5896045921 Reorder the terms: 0.5896045921 + -1.535714286x + x2 = 0.5357142857 + 0.5896045921 Combine like terms: 0.5357142857 + 0.5896045921 = 1.1253188778 0.5896045921 + -1.535714286x + x2 = 1.1253188778 Factor a perfect square on the left side: (x + -0.767857143)(x + -0.767857143) = 1.1253188778 Calculate the square root of the right side: 1.060810482 Break this problem into two subproblems by setting (x + -0.767857143) equal to 1.060810482 and -1.060810482.Subproblem 1
x + -0.767857143 = 1.060810482 Simplifying x + -0.767857143 = 1.060810482 Reorder the terms: -0.767857143 + x = 1.060810482 Solving -0.767857143 + x = 1.060810482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.767857143' to each side of the equation. -0.767857143 + 0.767857143 + x = 1.060810482 + 0.767857143 Combine like terms: -0.767857143 + 0.767857143 = 0.000000000 0.000000000 + x = 1.060810482 + 0.767857143 x = 1.060810482 + 0.767857143 Combine like terms: 1.060810482 + 0.767857143 = 1.828667625 x = 1.828667625 Simplifying x = 1.828667625Subproblem 2
x + -0.767857143 = -1.060810482 Simplifying x + -0.767857143 = -1.060810482 Reorder the terms: -0.767857143 + x = -1.060810482 Solving -0.767857143 + x = -1.060810482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.767857143' to each side of the equation. -0.767857143 + 0.767857143 + x = -1.060810482 + 0.767857143 Combine like terms: -0.767857143 + 0.767857143 = 0.000000000 0.000000000 + x = -1.060810482 + 0.767857143 x = -1.060810482 + 0.767857143 Combine like terms: -1.060810482 + 0.767857143 = -0.292953339 x = -0.292953339 Simplifying x = -0.292953339Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.828667625, -0.292953339}
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