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Simplifying -3x(x + -3) + 5(x + 7) + -1x(x + 1) + -2x + 7 + 4 = 0 Reorder the terms: -3x(-3 + x) + 5(x + 7) + -1x(x + 1) + -2x + 7 + 4 = 0 (-3 * -3x + x * -3x) + 5(x + 7) + -1x(x + 1) + -2x + 7 + 4 = 0 (9x + -3x2) + 5(x + 7) + -1x(x + 1) + -2x + 7 + 4 = 0 Reorder the terms: 9x + -3x2 + 5(7 + x) + -1x(x + 1) + -2x + 7 + 4 = 0 9x + -3x2 + (7 * 5 + x * 5) + -1x(x + 1) + -2x + 7 + 4 = 0 9x + -3x2 + (35 + 5x) + -1x(x + 1) + -2x + 7 + 4 = 0 Reorder the terms: 9x + -3x2 + 35 + 5x + -1x(1 + x) + -2x + 7 + 4 = 0 9x + -3x2 + 35 + 5x + (1 * -1x + x * -1x) + -2x + 7 + 4 = 0 9x + -3x2 + 35 + 5x + (-1x + -1x2) + -2x + 7 + 4 = 0 Reorder the terms: 35 + 7 + 4 + 9x + 5x + -1x + -2x + -3x2 + -1x2 = 0 Combine like terms: 35 + 7 = 42 42 + 4 + 9x + 5x + -1x + -2x + -3x2 + -1x2 = 0 Combine like terms: 42 + 4 = 46 46 + 9x + 5x + -1x + -2x + -3x2 + -1x2 = 0 Combine like terms: 9x + 5x = 14x 46 + 14x + -1x + -2x + -3x2 + -1x2 = 0 Combine like terms: 14x + -1x = 13x 46 + 13x + -2x + -3x2 + -1x2 = 0 Combine like terms: 13x + -2x = 11x 46 + 11x + -3x2 + -1x2 = 0 Combine like terms: -3x2 + -1x2 = -4x2 46 + 11x + -4x2 = 0 Solving 46 + 11x + -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'. -11.5 + -2.75x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -2.75x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -2.75x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -2.75x + x2 = 0 + 11.5 -2.75x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -2.75x + x2 = 11.5 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 11.5 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 11.5 + 1.890625 Combine like terms: 11.5 + 1.890625 = 13.390625 1.890625 + -2.75x + x2 = 13.390625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 13.390625 Calculate the square root of the right side: 3.659320292 Break this problem into two subproblems by setting (x + -1.375) equal to 3.659320292 and -3.659320292.Subproblem 1
x + -1.375 = 3.659320292 Simplifying x + -1.375 = 3.659320292 Reorder the terms: -1.375 + x = 3.659320292 Solving -1.375 + x = 3.659320292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 3.659320292 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 3.659320292 + 1.375 x = 3.659320292 + 1.375 Combine like terms: 3.659320292 + 1.375 = 5.034320292 x = 5.034320292 Simplifying x = 5.034320292Subproblem 2
x + -1.375 = -3.659320292 Simplifying x + -1.375 = -3.659320292 Reorder the terms: -1.375 + x = -3.659320292 Solving -1.375 + x = -3.659320292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -3.659320292 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -3.659320292 + 1.375 x = -3.659320292 + 1.375 Combine like terms: -3.659320292 + 1.375 = -2.284320292 x = -2.284320292 Simplifying x = -2.284320292Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.034320292, -2.284320292}
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