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Simplifying 3(x + 4) + 5x = -7 + 2x(x + -4) Reorder the terms: 3(4 + x) + 5x = -7 + 2x(x + -4) (4 * 3 + x * 3) + 5x = -7 + 2x(x + -4) (12 + 3x) + 5x = -7 + 2x(x + -4) Combine like terms: 3x + 5x = 8x 12 + 8x = -7 + 2x(x + -4) Reorder the terms: 12 + 8x = -7 + 2x(-4 + x) 12 + 8x = -7 + (-4 * 2x + x * 2x) 12 + 8x = -7 + (-8x + 2x2) Solving 12 + 8x = -7 + -8x + 2x2 Solving for variable 'x'. Reorder the terms: 12 + 7 + 8x + 8x + -2x2 = -7 + -8x + 2x2 + 7 + 8x + -2x2 Combine like terms: 12 + 7 = 19 19 + 8x + 8x + -2x2 = -7 + -8x + 2x2 + 7 + 8x + -2x2 Combine like terms: 8x + 8x = 16x 19 + 16x + -2x2 = -7 + -8x + 2x2 + 7 + 8x + -2x2 Reorder the terms: 19 + 16x + -2x2 = -7 + 7 + -8x + 8x + 2x2 + -2x2 Combine like terms: -7 + 7 = 0 19 + 16x + -2x2 = 0 + -8x + 8x + 2x2 + -2x2 19 + 16x + -2x2 = -8x + 8x + 2x2 + -2x2 Combine like terms: -8x + 8x = 0 19 + 16x + -2x2 = 0 + 2x2 + -2x2 19 + 16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 19 + 16x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -9.5 + -8x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + -8x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + -8x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + -8x + x2 = 0 + 9.5 -8x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 -8x + x2 = 9.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 9.5 + 16 Reorder the terms: 16 + -8x + x2 = 9.5 + 16 Combine like terms: 9.5 + 16 = 25.5 16 + -8x + x2 = 25.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 25.5 Calculate the square root of the right side: 5.049752469 Break this problem into two subproblems by setting (x + -4) equal to 5.049752469 and -5.049752469.Subproblem 1
x + -4 = 5.049752469 Simplifying x + -4 = 5.049752469 Reorder the terms: -4 + x = 5.049752469 Solving -4 + x = 5.049752469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.049752469 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.049752469 + 4 x = 5.049752469 + 4 Combine like terms: 5.049752469 + 4 = 9.049752469 x = 9.049752469 Simplifying x = 9.049752469Subproblem 2
x + -4 = -5.049752469 Simplifying x + -4 = -5.049752469 Reorder the terms: -4 + x = -5.049752469 Solving -4 + x = -5.049752469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.049752469 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.049752469 + 4 x = -5.049752469 + 4 Combine like terms: -5.049752469 + 4 = -1.049752469 x = -1.049752469 Simplifying x = -1.049752469Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.049752469, -1.049752469}
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