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Simplifying 1.5x2 + 2.5x + -1 = 126 Reorder the terms: -1 + 2.5x + 1.5x2 = 126 Solving -1 + 2.5x + 1.5x2 = 126 Solving for variable 'x'. Reorder the terms: -1 + -126 + 2.5x + 1.5x2 = 126 + -126 Combine like terms: -1 + -126 = -127 -127 + 2.5x + 1.5x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -127 + 2.5x + 1.5x2 = 0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -84.66666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '84.66666667' to each side of the equation. -84.66666667 + 1.666666667x + 84.66666667 + x2 = 0 + 84.66666667 Reorder the terms: -84.66666667 + 84.66666667 + 1.666666667x + x2 = 0 + 84.66666667 Combine like terms: -84.66666667 + 84.66666667 = 0.00000000 0.00000000 + 1.666666667x + x2 = 0 + 84.66666667 1.666666667x + x2 = 0 + 84.66666667 Combine like terms: 0 + 84.66666667 = 84.66666667 1.666666667x + x2 = 84.66666667 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 84.66666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 84.66666667 + 0.6944444447 Combine like terms: 84.66666667 + 0.6944444447 = 85.3611111147 0.6944444447 + 1.666666667x + x2 = 85.3611111147 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 85.3611111147 Calculate the square root of the right side: 9.239107701 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 9.239107701 and -9.239107701.Subproblem 1
x + 0.8333333335 = 9.239107701 Simplifying x + 0.8333333335 = 9.239107701 Reorder the terms: 0.8333333335 + x = 9.239107701 Solving 0.8333333335 + x = 9.239107701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 9.239107701 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 9.239107701 + -0.8333333335 x = 9.239107701 + -0.8333333335 Combine like terms: 9.239107701 + -0.8333333335 = 8.4057743675 x = 8.4057743675 Simplifying x = 8.4057743675Subproblem 2
x + 0.8333333335 = -9.239107701 Simplifying x + 0.8333333335 = -9.239107701 Reorder the terms: 0.8333333335 + x = -9.239107701 Solving 0.8333333335 + x = -9.239107701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -9.239107701 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -9.239107701 + -0.8333333335 x = -9.239107701 + -0.8333333335 Combine like terms: -9.239107701 + -0.8333333335 = -10.0724410345 x = -10.0724410345 Simplifying x = -10.0724410345Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.4057743675, -10.0724410345}
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