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Simplifying 10x2 + 5x + -7 = 0 Reorder the terms: -7 + 5x + 10x2 = 0 Solving -7 + 5x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + 0.5x + 0.7 + x2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + 0.5x + x2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + 0.5x + x2 = 0 + 0.7 0.5x + x2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 0.5x + x2 = 0.7 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.7 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.7 + 0.0625 Combine like terms: 0.7 + 0.0625 = 0.7625 0.0625 + 0.5x + x2 = 0.7625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.7625 Calculate the square root of the right side: 0.87321246 Break this problem into two subproblems by setting (x + 0.25) equal to 0.87321246 and -0.87321246.Subproblem 1
x + 0.25 = 0.87321246 Simplifying x + 0.25 = 0.87321246 Reorder the terms: 0.25 + x = 0.87321246 Solving 0.25 + x = 0.87321246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.87321246 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.87321246 + -0.25 x = 0.87321246 + -0.25 Combine like terms: 0.87321246 + -0.25 = 0.62321246 x = 0.62321246 Simplifying x = 0.62321246Subproblem 2
x + 0.25 = -0.87321246 Simplifying x + 0.25 = -0.87321246 Reorder the terms: 0.25 + x = -0.87321246 Solving 0.25 + x = -0.87321246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.87321246 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.87321246 + -0.25 x = -0.87321246 + -0.25 Combine like terms: -0.87321246 + -0.25 = -1.12321246 x = -1.12321246 Simplifying x = -1.12321246Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.62321246, -1.12321246}
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