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Simplifying 4x2 + 10x + -7 = 0 Reorder the terms: -7 + 10x + 4x2 = 0 Solving -7 + 10x + 4x2 = 0 Solving for variable 'x'. 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 = 0.570027472 x = 0.570027472 Simplifying x = 0.570027472Subproblem 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 = -3.070027472 x = -3.070027472 Simplifying x = -3.070027472Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.570027472, -3.070027472}
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