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Simplifying 5x2 + -7x = 96 Reorder the terms: -7x + 5x2 = 96 Solving -7x + 5x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + -7x + 5x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -19.2 + -1.4x + x2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + -1.4x + 19.2 + x2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + -1.4x + x2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + -1.4x + x2 = 0 + 19.2 -1.4x + x2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 -1.4x + x2 = 19.2 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 = 19.2 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 19.2 + 0.49 Combine like terms: 19.2 + 0.49 = 19.69 0.49 + -1.4x + x2 = 19.69 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 19.69 Calculate the square root of the right side: 4.437341546 Break this problem into two subproblems by setting (x + -0.7) equal to 4.437341546 and -4.437341546.Subproblem 1
x + -0.7 = 4.437341546 Simplifying x + -0.7 = 4.437341546 Reorder the terms: -0.7 + x = 4.437341546 Solving -0.7 + x = 4.437341546 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 = 4.437341546 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 4.437341546 + 0.7 x = 4.437341546 + 0.7 Combine like terms: 4.437341546 + 0.7 = 5.137341546 x = 5.137341546 Simplifying x = 5.137341546Subproblem 2
x + -0.7 = -4.437341546 Simplifying x + -0.7 = -4.437341546 Reorder the terms: -0.7 + x = -4.437341546 Solving -0.7 + x = -4.437341546 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 = -4.437341546 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -4.437341546 + 0.7 x = -4.437341546 + 0.7 Combine like terms: -4.437341546 + 0.7 = -3.737341546 x = -3.737341546 Simplifying x = -3.737341546Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.137341546, -3.737341546}
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