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Simplifying -4x2 + -7x + 20 = 0 Reorder the terms: 20 + -7x + -4x2 = 0 Solving 20 + -7x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5 + 1.75x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 1.75x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 1.75x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 1.75x + x2 = 0 + 5 1.75x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 1.75x + x2 = 5 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 = 5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 5 + 0.765625 Combine like terms: 5 + 0.765625 = 5.765625 0.765625 + 1.75x + x2 = 5.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 5.765625 Calculate the square root of the right side: 2.401171589 Break this problem into two subproblems by setting (x + 0.875) equal to 2.401171589 and -2.401171589.Subproblem 1
x + 0.875 = 2.401171589 Simplifying x + 0.875 = 2.401171589 Reorder the terms: 0.875 + x = 2.401171589 Solving 0.875 + x = 2.401171589 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 = 2.401171589 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.401171589 + -0.875 x = 2.401171589 + -0.875 Combine like terms: 2.401171589 + -0.875 = 1.526171589 x = 1.526171589 Simplifying x = 1.526171589Subproblem 2
x + 0.875 = -2.401171589 Simplifying x + 0.875 = -2.401171589 Reorder the terms: 0.875 + x = -2.401171589 Solving 0.875 + x = -2.401171589 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 = -2.401171589 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.401171589 + -0.875 x = -2.401171589 + -0.875 Combine like terms: -2.401171589 + -0.875 = -3.276171589 x = -3.276171589 Simplifying x = -3.276171589Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.526171589, -3.276171589}
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