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Simplifying 5 + -1(x + -3)(x + 3) = (x + 4) + -3x Reorder the terms: 5 + -1(-3 + x)(x + 3) = (x + 4) + -3x Reorder the terms: 5 + -1(-3 + x)(3 + x) = (x + 4) + -3x Multiply (-3 + x) * (3 + x) 5 + -1(-3(3 + x) + x(3 + x)) = (x + 4) + -3x 5 + -1((3 * -3 + x * -3) + x(3 + x)) = (x + 4) + -3x 5 + -1((-9 + -3x) + x(3 + x)) = (x + 4) + -3x 5 + -1(-9 + -3x + (3 * x + x * x)) = (x + 4) + -3x 5 + -1(-9 + -3x + (3x + x2)) = (x + 4) + -3x Combine like terms: -3x + 3x = 0 5 + -1(-9 + 0 + x2) = (x + 4) + -3x 5 + -1(-9 + x2) = (x + 4) + -3x 5 + (-9 * -1 + x2 * -1) = (x + 4) + -3x 5 + (9 + -1x2) = (x + 4) + -3x Combine like terms: 5 + 9 = 14 14 + -1x2 = (x + 4) + -3x Reorder the terms: 14 + -1x2 = (4 + x) + -3x Remove parenthesis around (4 + x) 14 + -1x2 = 4 + x + -3x Combine like terms: x + -3x = -2x 14 + -1x2 = 4 + -2x Solving 14 + -1x2 = 4 + -2x Solving for variable 'x'. Reorder the terms: 14 + -4 + 2x + -1x2 = 4 + -2x + -4 + 2x Combine like terms: 14 + -4 = 10 10 + 2x + -1x2 = 4 + -2x + -4 + 2x Reorder the terms: 10 + 2x + -1x2 = 4 + -4 + -2x + 2x Combine like terms: 4 + -4 = 0 10 + 2x + -1x2 = 0 + -2x + 2x 10 + 2x + -1x2 = -2x + 2x Combine like terms: -2x + 2x = 0 10 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -2x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -2x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -2x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2x + x2 = 0 + 10 -2x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -2x + x2 = 10 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 10 + 1 Reorder the terms: 1 + -2x + x2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + -2x + x2 = 11 Factor a perfect square on the left side: (x + -1)(x + -1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -1) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -1 = 3.31662479 Simplifying x + -1 = 3.31662479 Reorder the terms: -1 + x = 3.31662479 Solving -1 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.31662479 + 1 x = 3.31662479 + 1 Combine like terms: 3.31662479 + 1 = 4.31662479 x = 4.31662479 Simplifying x = 4.31662479Subproblem 2
x + -1 = -3.31662479 Simplifying x + -1 = -3.31662479 Reorder the terms: -1 + x = -3.31662479 Solving -1 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.31662479 + 1 x = -3.31662479 + 1 Combine like terms: -3.31662479 + 1 = -2.31662479 x = -2.31662479 Simplifying x = -2.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.31662479, -2.31662479}
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