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Simplifying 5x + 60 = (2x + -10)(2x + -10) Reorder the terms: 60 + 5x = (2x + -10)(2x + -10) Reorder the terms: 60 + 5x = (-10 + 2x)(2x + -10) Reorder the terms: 60 + 5x = (-10 + 2x)(-10 + 2x) Multiply (-10 + 2x) * (-10 + 2x) 60 + 5x = (-10(-10 + 2x) + 2x * (-10 + 2x)) 60 + 5x = ((-10 * -10 + 2x * -10) + 2x * (-10 + 2x)) 60 + 5x = ((100 + -20x) + 2x * (-10 + 2x)) 60 + 5x = (100 + -20x + (-10 * 2x + 2x * 2x)) 60 + 5x = (100 + -20x + (-20x + 4x2)) Combine like terms: -20x + -20x = -40x 60 + 5x = (100 + -40x + 4x2) Solving 60 + 5x = 100 + -40x + 4x2 Solving for variable 'x'. Reorder the terms: 60 + -100 + 5x + 40x + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2 Combine like terms: 60 + -100 = -40 -40 + 5x + 40x + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2 Combine like terms: 5x + 40x = 45x -40 + 45x + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2 Reorder the terms: -40 + 45x + -4x2 = 100 + -100 + -40x + 40x + 4x2 + -4x2 Combine like terms: 100 + -100 = 0 -40 + 45x + -4x2 = 0 + -40x + 40x + 4x2 + -4x2 -40 + 45x + -4x2 = -40x + 40x + 4x2 + -4x2 Combine like terms: -40x + 40x = 0 -40 + 45x + -4x2 = 0 + 4x2 + -4x2 -40 + 45x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -40 + 45x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 10 + -11.25x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -11.25x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -11.25x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -11.25x + x2 = 0 + -10 -11.25x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -11.25x + x2 = -10 The x term is -11.25x. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25x + 31.640625 + x2 = -10 + 31.640625 Reorder the terms: 31.640625 + -11.25x + x2 = -10 + 31.640625 Combine like terms: -10 + 31.640625 = 21.640625 31.640625 + -11.25x + x2 = 21.640625 Factor a perfect square on the left side: (x + -5.625)(x + -5.625) = 21.640625 Calculate the square root of the right side: 4.651948516 Break this problem into two subproblems by setting (x + -5.625) equal to 4.651948516 and -4.651948516.Subproblem 1
x + -5.625 = 4.651948516 Simplifying x + -5.625 = 4.651948516 Reorder the terms: -5.625 + x = 4.651948516 Solving -5.625 + x = 4.651948516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = 4.651948516 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = 4.651948516 + 5.625 x = 4.651948516 + 5.625 Combine like terms: 4.651948516 + 5.625 = 10.276948516 x = 10.276948516 Simplifying x = 10.276948516Subproblem 2
x + -5.625 = -4.651948516 Simplifying x + -5.625 = -4.651948516 Reorder the terms: -5.625 + x = -4.651948516 Solving -5.625 + x = -4.651948516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = -4.651948516 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = -4.651948516 + 5.625 x = -4.651948516 + 5.625 Combine like terms: -4.651948516 + 5.625 = 0.973051484 x = 0.973051484 Simplifying x = 0.973051484Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.276948516, 0.973051484}
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