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Simplifying 10 = (3 + -2x)(5 + -2x) Multiply (3 + -2x) * (5 + -2x) 10 = (3(5 + -2x) + -2x * (5 + -2x)) 10 = ((5 * 3 + -2x * 3) + -2x * (5 + -2x)) 10 = ((15 + -6x) + -2x * (5 + -2x)) 10 = (15 + -6x + (5 * -2x + -2x * -2x)) 10 = (15 + -6x + (-10x + 4x2)) Combine like terms: -6x + -10x = -16x 10 = (15 + -16x + 4x2) Solving 10 = 15 + -16x + 4x2 Solving for variable 'x'. Combine like terms: 10 + -15 = -5 -5 + 16x + -4x2 = 15 + -16x + 4x2 + -15 + 16x + -4x2 Reorder the terms: -5 + 16x + -4x2 = 15 + -15 + -16x + 16x + 4x2 + -4x2 Combine like terms: 15 + -15 = 0 -5 + 16x + -4x2 = 0 + -16x + 16x + 4x2 + -4x2 -5 + 16x + -4x2 = -16x + 16x + 4x2 + -4x2 Combine like terms: -16x + 16x = 0 -5 + 16x + -4x2 = 0 + 4x2 + -4x2 -5 + 16x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5 + 16x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.25 + -4x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -4x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -4x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -4x + x2 = 0 + -1.25 -4x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -4x + x2 = -1.25 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -1.25 + 4 Reorder the terms: 4 + -4x + x2 = -1.25 + 4 Combine like terms: -1.25 + 4 = 2.75 4 + -4x + x2 = 2.75 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + -2) equal to 1.658312395 and -1.658312395.Subproblem 1
x + -2 = 1.658312395 Simplifying x + -2 = 1.658312395 Reorder the terms: -2 + x = 1.658312395 Solving -2 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.658312395 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.658312395 + 2 x = 1.658312395 + 2 Combine like terms: 1.658312395 + 2 = 3.658312395 x = 3.658312395 Simplifying x = 3.658312395Subproblem 2
x + -2 = -1.658312395 Simplifying x + -2 = -1.658312395 Reorder the terms: -2 + x = -1.658312395 Solving -2 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.658312395 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.658312395 + 2 x = -1.658312395 + 2 Combine like terms: -1.658312395 + 2 = 0.341687605 x = 0.341687605 Simplifying x = 0.341687605Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.658312395, 0.341687605}
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