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Simplifying 5x2 = 70 + 7x Solving 5x2 = 70 + 7x Solving for variable 'x'. Reorder the terms: -70 + -7x + 5x2 = 70 + 7x + -70 + -7x Reorder the terms: -70 + -7x + 5x2 = 70 + -70 + 7x + -7x Combine like terms: 70 + -70 = 0 -70 + -7x + 5x2 = 0 + 7x + -7x -70 + -7x + 5x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -70 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14 + -1.4x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -1.4x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -1.4x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1.4x + x2 = 0 + 14 -1.4x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -1.4x + x2 = 14 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 = 14 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 14 + 0.49 Combine like terms: 14 + 0.49 = 14.49 0.49 + -1.4x + x2 = 14.49 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 14.49 Calculate the square root of the right side: 3.806573262 Break this problem into two subproblems by setting (x + -0.7) equal to 3.806573262 and -3.806573262.Subproblem 1
x + -0.7 = 3.806573262 Simplifying x + -0.7 = 3.806573262 Reorder the terms: -0.7 + x = 3.806573262 Solving -0.7 + x = 3.806573262 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 = 3.806573262 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 3.806573262 + 0.7 x = 3.806573262 + 0.7 Combine like terms: 3.806573262 + 0.7 = 4.506573262 x = 4.506573262 Simplifying x = 4.506573262Subproblem 2
x + -0.7 = -3.806573262 Simplifying x + -0.7 = -3.806573262 Reorder the terms: -0.7 + x = -3.806573262 Solving -0.7 + x = -3.806573262 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 = -3.806573262 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -3.806573262 + 0.7 x = -3.806573262 + 0.7 Combine like terms: -3.806573262 + 0.7 = -3.106573262 x = -3.106573262 Simplifying x = -3.106573262Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.506573262, -3.106573262}
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