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Simplifying (5x)(5x + -7) = 24 Remove parenthesis around (5x) 5x(5x + -7) = 24 Reorder the terms: 5x(-7 + 5x) = 24 (-7 * 5x + 5x * 5x) = 24 (-35x + 25x2) = 24 Solving -35x + 25x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + -35x + 25x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -35x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.96 + -1.4x + x2 = 0 Move the constant term to the right: Add '0.96' to each side of the equation. -0.96 + -1.4x + 0.96 + x2 = 0 + 0.96 Reorder the terms: -0.96 + 0.96 + -1.4x + x2 = 0 + 0.96 Combine like terms: -0.96 + 0.96 = 0.00 0.00 + -1.4x + x2 = 0 + 0.96 -1.4x + x2 = 0 + 0.96 Combine like terms: 0 + 0.96 = 0.96 -1.4x + x2 = 0.96 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 0.96 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 0.96 + 0.49 Combine like terms: 0.96 + 0.49 = 1.45 0.49 + -1.4x + x2 = 1.45 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (x + -0.7) equal to 1.204159458 and -1.204159458.Subproblem 1
x + -0.7 = 1.204159458 Simplifying x + -0.7 = 1.204159458 Reorder the terms: -0.7 + x = 1.204159458 Solving -0.7 + x = 1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 1.204159458 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.204159458 + 0.7 x = 1.204159458 + 0.7 Combine like terms: 1.204159458 + 0.7 = 1.904159458 x = 1.904159458 Simplifying x = 1.904159458Subproblem 2
x + -0.7 = -1.204159458 Simplifying x + -0.7 = -1.204159458 Reorder the terms: -0.7 + x = -1.204159458 Solving -0.7 + x = -1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -1.204159458 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.204159458 + 0.7 x = -1.204159458 + 0.7 Combine like terms: -1.204159458 + 0.7 = -0.504159458 x = -0.504159458 Simplifying x = -0.504159458Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.904159458, -0.504159458}
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