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Simplifying 4x(2x + -5) = 7 Reorder the terms: 4x(-5 + 2x) = 7 (-5 * 4x + 2x * 4x) = 7 (-20x + 8x2) = 7 Solving -20x + 8x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -20x + 8x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -2.5x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -2.5x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -2.5x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -2.5x + x2 = 0 + 0.875 -2.5x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -2.5x + x2 = 0.875 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 = 0.875 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 0.875 + 1.5625 Combine like terms: 0.875 + 1.5625 = 2.4375 1.5625 + -2.5x + x2 = 2.4375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.4375 Calculate the square root of the right side: 1.5612495 Break this problem into two subproblems by setting (x + -1.25) equal to 1.5612495 and -1.5612495.Subproblem 1
x + -1.25 = 1.5612495 Simplifying x + -1.25 = 1.5612495 Reorder the terms: -1.25 + x = 1.5612495 Solving -1.25 + x = 1.5612495 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 = 1.5612495 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.5612495 + 1.25 x = 1.5612495 + 1.25 Combine like terms: 1.5612495 + 1.25 = 2.8112495 x = 2.8112495 Simplifying x = 2.8112495Subproblem 2
x + -1.25 = -1.5612495 Simplifying x + -1.25 = -1.5612495 Reorder the terms: -1.25 + x = -1.5612495 Solving -1.25 + x = -1.5612495 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 = -1.5612495 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.5612495 + 1.25 x = -1.5612495 + 1.25 Combine like terms: -1.5612495 + 1.25 = -0.3112495 x = -0.3112495 Simplifying x = -0.3112495Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8112495, -0.3112495}
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