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Simplifying (7x + -21)(5x + 13) = 360 Reorder the terms: (-21 + 7x)(5x + 13) = 360 Reorder the terms: (-21 + 7x)(13 + 5x) = 360 Multiply (-21 + 7x) * (13 + 5x) (-21(13 + 5x) + 7x * (13 + 5x)) = 360 ((13 * -21 + 5x * -21) + 7x * (13 + 5x)) = 360 ((-273 + -105x) + 7x * (13 + 5x)) = 360 (-273 + -105x + (13 * 7x + 5x * 7x)) = 360 (-273 + -105x + (91x + 35x2)) = 360 Combine like terms: -105x + 91x = -14x (-273 + -14x + 35x2) = 360 Solving -273 + -14x + 35x2 = 360 Solving for variable 'x'. Reorder the terms: -273 + -360 + -14x + 35x2 = 360 + -360 Combine like terms: -273 + -360 = -633 -633 + -14x + 35x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -633 + -14x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -18.08571429 + -0.4x + x2 = 0 Move the constant term to the right: Add '18.08571429' to each side of the equation. -18.08571429 + -0.4x + 18.08571429 + x2 = 0 + 18.08571429 Reorder the terms: -18.08571429 + 18.08571429 + -0.4x + x2 = 0 + 18.08571429 Combine like terms: -18.08571429 + 18.08571429 = 0.00000000 0.00000000 + -0.4x + x2 = 0 + 18.08571429 -0.4x + x2 = 0 + 18.08571429 Combine like terms: 0 + 18.08571429 = 18.08571429 -0.4x + x2 = 18.08571429 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 18.08571429 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 18.08571429 + 0.04 Combine like terms: 18.08571429 + 0.04 = 18.12571429 0.04 + -0.4x + x2 = 18.12571429 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 18.12571429 Calculate the square root of the right side: 4.25743048 Break this problem into two subproblems by setting (x + -0.2) equal to 4.25743048 and -4.25743048.Subproblem 1
x + -0.2 = 4.25743048 Simplifying x + -0.2 = 4.25743048 Reorder the terms: -0.2 + x = 4.25743048 Solving -0.2 + x = 4.25743048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 4.25743048 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 4.25743048 + 0.2 x = 4.25743048 + 0.2 Combine like terms: 4.25743048 + 0.2 = 4.45743048 x = 4.45743048 Simplifying x = 4.45743048Subproblem 2
x + -0.2 = -4.25743048 Simplifying x + -0.2 = -4.25743048 Reorder the terms: -0.2 + x = -4.25743048 Solving -0.2 + x = -4.25743048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -4.25743048 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -4.25743048 + 0.2 x = -4.25743048 + 0.2 Combine like terms: -4.25743048 + 0.2 = -4.05743048 x = -4.05743048 Simplifying x = -4.05743048Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.45743048, -4.05743048}
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