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Simplifying 90 = x2 + 1.75x Reorder the terms: 90 = 1.75x + x2 Solving 90 = 1.75x + x2 Solving for variable 'x'. Reorder the terms: 90 + -1.75x + -1x2 = 1.75x + -1.75x + x2 + -1x2 Combine like terms: 1.75x + -1.75x = 0.00 90 + -1.75x + -1x2 = 0.00 + x2 + -1x2 90 + -1.75x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 90 + -1.75x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -90 + 1.75x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 1.75x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 1.75x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 1.75x + x2 = 0 + 90 1.75x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 1.75x + x2 = 90 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 90 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 90 + 0.765625 Combine like terms: 90 + 0.765625 = 90.765625 0.765625 + 1.75x + x2 = 90.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 90.765625 Calculate the square root of the right side: 9.527099506 Break this problem into two subproblems by setting (x + 0.875) equal to 9.527099506 and -9.527099506.Subproblem 1
x + 0.875 = 9.527099506 Simplifying x + 0.875 = 9.527099506 Reorder the terms: 0.875 + x = 9.527099506 Solving 0.875 + x = 9.527099506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 9.527099506 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 9.527099506 + -0.875 x = 9.527099506 + -0.875 Combine like terms: 9.527099506 + -0.875 = 8.652099506 x = 8.652099506 Simplifying x = 8.652099506Subproblem 2
x + 0.875 = -9.527099506 Simplifying x + 0.875 = -9.527099506 Reorder the terms: 0.875 + x = -9.527099506 Solving 0.875 + x = -9.527099506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -9.527099506 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -9.527099506 + -0.875 x = -9.527099506 + -0.875 Combine like terms: -9.527099506 + -0.875 = -10.402099506 x = -10.402099506 Simplifying x = -10.402099506Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.652099506, -10.402099506}
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