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Simplifying 10x2 + 10x + -7 = 0 Reorder the terms: -7 + 10x + 10x2 = 0 Solving -7 + 10x + 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 + x + x2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + x + 0.7 + x2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + x + x2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x + x2 = 0 + 0.7 x + x2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 x + x2 = 0.7 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.7 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.7 + 0.25 Combine like terms: 0.7 + 0.25 = 0.95 1.25 + x2 = 0.95 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.95 Calculate the square root of the right side: 0.974679434 Break this problem into two subproblems by setting (x + 0.5) equal to 0.974679434 and -0.974679434.Subproblem 1
x + 0.5 = 0.974679434 Simplifying x + 0.5 = 0.974679434 Reorder the terms: 0.5 + x = 0.974679434 Solving 0.5 + x = 0.974679434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.974679434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.974679434 + -0.5 x = 0.974679434 + -0.5 Combine like terms: 0.974679434 + -0.5 = 0.474679434 x = 0.474679434 Simplifying x = 0.474679434Subproblem 2
x + 0.5 = -0.974679434 Simplifying x + 0.5 = -0.974679434 Reorder the terms: 0.5 + x = -0.974679434 Solving 0.5 + x = -0.974679434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.974679434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.974679434 + -0.5 x = -0.974679434 + -0.5 Combine like terms: -0.974679434 + -0.5 = -1.474679434 x = -1.474679434 Simplifying x = -1.474679434Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.474679434, -1.474679434}
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