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Simplifying 2 + -4x(x + 4) = x + -3(x + 5) Reorder the terms: 2 + -4x(4 + x) = x + -3(x + 5) 2 + (4 * -4x + x * -4x) = x + -3(x + 5) 2 + (-16x + -4x2) = x + -3(x + 5) Reorder the terms: 2 + -16x + -4x2 = x + -3(5 + x) 2 + -16x + -4x2 = x + (5 * -3 + x * -3) 2 + -16x + -4x2 = x + (-15 + -3x) Reorder the terms: 2 + -16x + -4x2 = -15 + x + -3x Combine like terms: x + -3x = -2x 2 + -16x + -4x2 = -15 + -2x Solving 2 + -16x + -4x2 = -15 + -2x Solving for variable 'x'. Reorder the terms: 2 + 15 + -16x + 2x + -4x2 = -15 + -2x + 15 + 2x Combine like terms: 2 + 15 = 17 17 + -16x + 2x + -4x2 = -15 + -2x + 15 + 2x Combine like terms: -16x + 2x = -14x 17 + -14x + -4x2 = -15 + -2x + 15 + 2x Reorder the terms: 17 + -14x + -4x2 = -15 + 15 + -2x + 2x Combine like terms: -15 + 15 = 0 17 + -14x + -4x2 = 0 + -2x + 2x 17 + -14x + -4x2 = -2x + 2x Combine like terms: -2x + 2x = 0 17 + -14x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -4.25 + 3.5x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + 3.5x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + 3.5x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + 3.5x + x2 = 0 + 4.25 3.5x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 3.5x + x2 = 4.25 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 4.25 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 4.25 + 3.0625 Combine like terms: 4.25 + 3.0625 = 7.3125 3.0625 + 3.5x + x2 = 7.3125 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 7.3125 Calculate the square root of the right side: 2.704163457 Break this problem into two subproblems by setting (x + 1.75) equal to 2.704163457 and -2.704163457.Subproblem 1
x + 1.75 = 2.704163457 Simplifying x + 1.75 = 2.704163457 Reorder the terms: 1.75 + x = 2.704163457 Solving 1.75 + x = 2.704163457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.704163457 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.704163457 + -1.75 x = 2.704163457 + -1.75 Combine like terms: 2.704163457 + -1.75 = 0.954163457 x = 0.954163457 Simplifying x = 0.954163457Subproblem 2
x + 1.75 = -2.704163457 Simplifying x + 1.75 = -2.704163457 Reorder the terms: 1.75 + x = -2.704163457 Solving 1.75 + x = -2.704163457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.704163457 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.704163457 + -1.75 x = -2.704163457 + -1.75 Combine like terms: -2.704163457 + -1.75 = -4.454163457 x = -4.454163457 Simplifying x = -4.454163457Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.954163457, -4.454163457}
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