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Simplifying (2x)(2x + -5) = 75 Remove parenthesis around (2x) 2x(2x + -5) = 75 Reorder the terms: 2x(-5 + 2x) = 75 (-5 * 2x + 2x * 2x) = 75 (-10x + 4x2) = 75 Solving -10x + 4x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + -10x + 4x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + -10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.75 + -2.5x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + -2.5x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + -2.5x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + -2.5x + x2 = 0 + 18.75 -2.5x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 -2.5x + x2 = 18.75 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 18.75 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 18.75 + 1.5625 Combine like terms: 18.75 + 1.5625 = 20.3125 1.5625 + -2.5x + x2 = 20.3125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 20.3125 Calculate the square root of the right side: 4.506939094 Break this problem into two subproblems by setting (x + -1.25) equal to 4.506939094 and -4.506939094.Subproblem 1
x + -1.25 = 4.506939094 Simplifying x + -1.25 = 4.506939094 Reorder the terms: -1.25 + x = 4.506939094 Solving -1.25 + x = 4.506939094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 4.506939094 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 4.506939094 + 1.25 x = 4.506939094 + 1.25 Combine like terms: 4.506939094 + 1.25 = 5.756939094 x = 5.756939094 Simplifying x = 5.756939094Subproblem 2
x + -1.25 = -4.506939094 Simplifying x + -1.25 = -4.506939094 Reorder the terms: -1.25 + x = -4.506939094 Solving -1.25 + x = -4.506939094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -4.506939094 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -4.506939094 + 1.25 x = -4.506939094 + 1.25 Combine like terms: -4.506939094 + 1.25 = -3.256939094 x = -3.256939094 Simplifying x = -3.256939094Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.756939094, -3.256939094}
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