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Simplifying 7 = (2x + -5)(2x) Reorder the terms: 7 = (-5 + 2x)(2x) Remove parenthesis around (2x) 7 = (-5 + 2x) * 2x Reorder the terms for easier multiplication: 7 = 2x(-5 + 2x) 7 = (-5 * 2x + 2x * 2x) 7 = (-10x + 4x2) Solving 7 = -10x + 4x2 Solving for variable 'x'. Reorder the terms: 7 + 10x + -4x2 = -10x + 10x + 4x2 + -4x2 Combine like terms: -10x + 10x = 0 7 + 10x + -4x2 = 0 + 4x2 + -4x2 7 + 10x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 7 + 10x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + -2.5x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -2.5x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -2.5x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -2.5x + x2 = 0 + 1.75 -2.5x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -2.5x + x2 = 1.75 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 = 1.75 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1.75 + 1.5625 Combine like terms: 1.75 + 1.5625 = 3.3125 1.5625 + -2.5x + x2 = 3.3125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 3.3125 Calculate the square root of the right side: 1.820027472 Break this problem into two subproblems by setting (x + -1.25) equal to 1.820027472 and -1.820027472.Subproblem 1
x + -1.25 = 1.820027472 Simplifying x + -1.25 = 1.820027472 Reorder the terms: -1.25 + x = 1.820027472 Solving -1.25 + x = 1.820027472 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 = 1.820027472 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.820027472 + 1.25 x = 1.820027472 + 1.25 Combine like terms: 1.820027472 + 1.25 = 3.070027472 x = 3.070027472 Simplifying x = 3.070027472Subproblem 2
x + -1.25 = -1.820027472 Simplifying x + -1.25 = -1.820027472 Reorder the terms: -1.25 + x = -1.820027472 Solving -1.25 + x = -1.820027472 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 = -1.820027472 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.820027472 + 1.25 x = -1.820027472 + 1.25 Combine like terms: -1.820027472 + 1.25 = -0.570027472 x = -0.570027472 Simplifying x = -0.570027472Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.070027472, -0.570027472}
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