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Simplifying x + -1(4x + -7) = 5x(x + 21) Reorder the terms: x + -1(-7 + 4x) = 5x(x + 21) x + (-7 * -1 + 4x * -1) = 5x(x + 21) x + (7 + -4x) = 5x(x + 21) Reorder the terms: 7 + x + -4x = 5x(x + 21) Combine like terms: x + -4x = -3x 7 + -3x = 5x(x + 21) Reorder the terms: 7 + -3x = 5x(21 + x) 7 + -3x = (21 * 5x + x * 5x) 7 + -3x = (105x + 5x2) Solving 7 + -3x = 105x + 5x2 Solving for variable 'x'. Combine like terms: -3x + -105x = -108x 7 + -108x + -5x2 = 105x + 5x2 + -105x + -5x2 Reorder the terms: 7 + -108x + -5x2 = 105x + -105x + 5x2 + -5x2 Combine like terms: 105x + -105x = 0 7 + -108x + -5x2 = 0 + 5x2 + -5x2 7 + -108x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 7 + -108x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.4 + 21.6x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 21.6x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 21.6x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 21.6x + x2 = 0 + 1.4 21.6x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 21.6x + x2 = 1.4 The x term is 21.6x. Take half its coefficient (10.8). Square it (116.64) and add it to both sides. Add '116.64' to each side of the equation. 21.6x + 116.64 + x2 = 1.4 + 116.64 Reorder the terms: 116.64 + 21.6x + x2 = 1.4 + 116.64 Combine like terms: 1.4 + 116.64 = 118.04 116.64 + 21.6x + x2 = 118.04 Factor a perfect square on the left side: (x + 10.8)(x + 10.8) = 118.04 Calculate the square root of the right side: 10.864621484 Break this problem into two subproblems by setting (x + 10.8) equal to 10.864621484 and -10.864621484.Subproblem 1
x + 10.8 = 10.864621484 Simplifying x + 10.8 = 10.864621484 Reorder the terms: 10.8 + x = 10.864621484 Solving 10.8 + x = 10.864621484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.8' to each side of the equation. 10.8 + -10.8 + x = 10.864621484 + -10.8 Combine like terms: 10.8 + -10.8 = 0.0 0.0 + x = 10.864621484 + -10.8 x = 10.864621484 + -10.8 Combine like terms: 10.864621484 + -10.8 = 0.064621484 x = 0.064621484 Simplifying x = 0.064621484Subproblem 2
x + 10.8 = -10.864621484 Simplifying x + 10.8 = -10.864621484 Reorder the terms: 10.8 + x = -10.864621484 Solving 10.8 + x = -10.864621484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.8' to each side of the equation. 10.8 + -10.8 + x = -10.864621484 + -10.8 Combine like terms: 10.8 + -10.8 = 0.0 0.0 + x = -10.864621484 + -10.8 x = -10.864621484 + -10.8 Combine like terms: -10.864621484 + -10.8 = -21.664621484 x = -21.664621484 Simplifying x = -21.664621484Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.064621484, -21.664621484}
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