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Simplifying (x + -3)(x + -3) + -5(10 + x) = x + -8 Reorder the terms: (-3 + x)(x + -3) + -5(10 + x) = x + -8 Reorder the terms: (-3 + x)(-3 + x) + -5(10 + x) = x + -8 Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x)) + -5(10 + x) = x + -8 ((-3 * -3 + x * -3) + x(-3 + x)) + -5(10 + x) = x + -8 ((9 + -3x) + x(-3 + x)) + -5(10 + x) = x + -8 (9 + -3x + (-3 * x + x * x)) + -5(10 + x) = x + -8 (9 + -3x + (-3x + x2)) + -5(10 + x) = x + -8 Combine like terms: -3x + -3x = -6x (9 + -6x + x2) + -5(10 + x) = x + -8 9 + -6x + x2 + (10 * -5 + x * -5) = x + -8 9 + -6x + x2 + (-50 + -5x) = x + -8 Reorder the terms: 9 + -50 + -6x + -5x + x2 = x + -8 Combine like terms: 9 + -50 = -41 -41 + -6x + -5x + x2 = x + -8 Combine like terms: -6x + -5x = -11x -41 + -11x + x2 = x + -8 Reorder the terms: -41 + -11x + x2 = -8 + x Solving -41 + -11x + x2 = -8 + x Solving for variable 'x'. Reorder the terms: -41 + 8 + -11x + -1x + x2 = -8 + x + 8 + -1x Combine like terms: -41 + 8 = -33 -33 + -11x + -1x + x2 = -8 + x + 8 + -1x Combine like terms: -11x + -1x = -12x -33 + -12x + x2 = -8 + x + 8 + -1x Reorder the terms: -33 + -12x + x2 = -8 + 8 + x + -1x Combine like terms: -8 + 8 = 0 -33 + -12x + x2 = 0 + x + -1x -33 + -12x + x2 = x + -1x Combine like terms: x + -1x = 0 -33 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -12x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + -12x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -12x + x2 = 0 + 33 -12x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 -12x + x2 = 33 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 33 + 36 Reorder the terms: 36 + -12x + x2 = 33 + 36 Combine like terms: 33 + 36 = 69 36 + -12x + x2 = 69 Factor a perfect square on the left side: (x + -6)(x + -6) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + -6) equal to 8.306623863 and -8.306623863.Subproblem 1
x + -6 = 8.306623863 Simplifying x + -6 = 8.306623863 Reorder the terms: -6 + x = 8.306623863 Solving -6 + x = 8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 8.306623863 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.306623863 + 6 x = 8.306623863 + 6 Combine like terms: 8.306623863 + 6 = 14.306623863 x = 14.306623863 Simplifying x = 14.306623863Subproblem 2
x + -6 = -8.306623863 Simplifying x + -6 = -8.306623863 Reorder the terms: -6 + x = -8.306623863 Solving -6 + x = -8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -8.306623863 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.306623863 + 6 x = -8.306623863 + 6 Combine like terms: -8.306623863 + 6 = -2.306623863 x = -2.306623863 Simplifying x = -2.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.306623863, -2.306623863}
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