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Simplifying 2x2 + 5x = 28.001 Reorder the terms: 5x + 2x2 = 28.001 Solving 5x + 2x2 = 28.001 Solving for variable 'x'. Reorder the terms: -28.001 + 5x + 2x2 = 28.001 + -28.001 Combine like terms: 28.001 + -28.001 = 0.000 -28.001 + 5x + 2x2 = 0.000 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14.0005 + 2.5x + x2 = 0.000 Move the constant term to the right: Add '14.0005' to each side of the equation. -14.0005 + 2.5x + 14.0005 + x2 = 0.000 + 14.0005 Reorder the terms: -14.0005 + 14.0005 + 2.5x + x2 = 0.000 + 14.0005 Combine like terms: -14.0005 + 14.0005 = 0.0000 0.0000 + 2.5x + x2 = 0.000 + 14.0005 2.5x + x2 = 0.000 + 14.0005 Combine like terms: 0.000 + 14.0005 = 14.0005 2.5x + x2 = 14.0005 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 14.0005 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 14.0005 + 1.5625 Combine like terms: 14.0005 + 1.5625 = 15.563 1.5625 + 2.5x + x2 = 15.563 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 15.563 Calculate the square root of the right side: 3.944996831 Break this problem into two subproblems by setting (x + 1.25) equal to 3.944996831 and -3.944996831.Subproblem 1
x + 1.25 = 3.944996831 Simplifying x + 1.25 = 3.944996831 Reorder the terms: 1.25 + x = 3.944996831 Solving 1.25 + x = 3.944996831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 3.944996831 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.944996831 + -1.25 x = 3.944996831 + -1.25 Combine like terms: 3.944996831 + -1.25 = 2.694996831 x = 2.694996831 Simplifying x = 2.694996831Subproblem 2
x + 1.25 = -3.944996831 Simplifying x + 1.25 = -3.944996831 Reorder the terms: 1.25 + x = -3.944996831 Solving 1.25 + x = -3.944996831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -3.944996831 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.944996831 + -1.25 x = -3.944996831 + -1.25 Combine like terms: -3.944996831 + -1.25 = -5.194996831 x = -5.194996831 Simplifying x = -5.194996831Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.694996831, -5.194996831}
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