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Simplifying 5x + 8 = 4x2 + -20x Reorder the terms: 8 + 5x = 4x2 + -20x Reorder the terms: 8 + 5x = -20x + 4x2 Solving 8 + 5x = -20x + 4x2 Solving for variable 'x'. Combine like terms: 5x + 20x = 25x 8 + 25x + -4x2 = -20x + 4x2 + 20x + -4x2 Reorder the terms: 8 + 25x + -4x2 = -20x + 20x + 4x2 + -4x2 Combine like terms: -20x + 20x = 0 8 + 25x + -4x2 = 0 + 4x2 + -4x2 8 + 25x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 8 + 25x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2 + -6.25x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -6.25x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -6.25x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6.25x + x2 = 0 + 2 -6.25x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6.25x + x2 = 2 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 2 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 2 + 9.765625 Combine like terms: 2 + 9.765625 = 11.765625 9.765625 + -6.25x + x2 = 11.765625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 11.765625 Calculate the square root of the right side: 3.430105684 Break this problem into two subproblems by setting (x + -3.125) equal to 3.430105684 and -3.430105684.Subproblem 1
x + -3.125 = 3.430105684 Simplifying x + -3.125 = 3.430105684 Reorder the terms: -3.125 + x = 3.430105684 Solving -3.125 + x = 3.430105684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 3.430105684 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.430105684 + 3.125 x = 3.430105684 + 3.125 Combine like terms: 3.430105684 + 3.125 = 6.555105684 x = 6.555105684 Simplifying x = 6.555105684Subproblem 2
x + -3.125 = -3.430105684 Simplifying x + -3.125 = -3.430105684 Reorder the terms: -3.125 + x = -3.430105684 Solving -3.125 + x = -3.430105684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -3.430105684 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.430105684 + 3.125 x = -3.430105684 + 3.125 Combine like terms: -3.430105684 + 3.125 = -0.305105684 x = -0.305105684 Simplifying x = -0.305105684Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.555105684, -0.305105684}
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