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Simplifying 5x2 + -7x = 100 Reorder the terms: -7x + 5x2 = 100 Solving -7x + 5x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + -7x + 5x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -20 + -1.4x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -1.4x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -1.4x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1.4x + x2 = 0 + 20 -1.4x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -1.4x + x2 = 20 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 20 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 20 + 0.49 Combine like terms: 20 + 0.49 = 20.49 0.49 + -1.4x + x2 = 20.49 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 20.49 Calculate the square root of the right side: 4.526588119 Break this problem into two subproblems by setting (x + -0.7) equal to 4.526588119 and -4.526588119.Subproblem 1
x + -0.7 = 4.526588119 Simplifying x + -0.7 = 4.526588119 Reorder the terms: -0.7 + x = 4.526588119 Solving -0.7 + x = 4.526588119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 4.526588119 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 4.526588119 + 0.7 x = 4.526588119 + 0.7 Combine like terms: 4.526588119 + 0.7 = 5.226588119 x = 5.226588119 Simplifying x = 5.226588119Subproblem 2
x + -0.7 = -4.526588119 Simplifying x + -0.7 = -4.526588119 Reorder the terms: -0.7 + x = -4.526588119 Solving -0.7 + x = -4.526588119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -4.526588119 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -4.526588119 + 0.7 x = -4.526588119 + 0.7 Combine like terms: -4.526588119 + 0.7 = -3.826588119 x = -3.826588119 Simplifying x = -3.826588119Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.226588119, -3.826588119}
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