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Simplifying 7x + 5 = 10x(x + -7) + -3 Reorder the terms: 5 + 7x = 10x(x + -7) + -3 Reorder the terms: 5 + 7x = 10x(-7 + x) + -3 5 + 7x = (-7 * 10x + x * 10x) + -3 5 + 7x = (-70x + 10x2) + -3 Reorder the terms: 5 + 7x = -3 + -70x + 10x2 Solving 5 + 7x = -3 + -70x + 10x2 Solving for variable 'x'. Reorder the terms: 5 + 3 + 7x + 70x + -10x2 = -3 + -70x + 10x2 + 3 + 70x + -10x2 Combine like terms: 5 + 3 = 8 8 + 7x + 70x + -10x2 = -3 + -70x + 10x2 + 3 + 70x + -10x2 Combine like terms: 7x + 70x = 77x 8 + 77x + -10x2 = -3 + -70x + 10x2 + 3 + 70x + -10x2 Reorder the terms: 8 + 77x + -10x2 = -3 + 3 + -70x + 70x + 10x2 + -10x2 Combine like terms: -3 + 3 = 0 8 + 77x + -10x2 = 0 + -70x + 70x + 10x2 + -10x2 8 + 77x + -10x2 = -70x + 70x + 10x2 + -10x2 Combine like terms: -70x + 70x = 0 8 + 77x + -10x2 = 0 + 10x2 + -10x2 8 + 77x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 8 + 77x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.8 + -7.7x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -7.7x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -7.7x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -7.7x + x2 = 0 + 0.8 -7.7x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -7.7x + x2 = 0.8 The x term is -7.7x. Take half its coefficient (-3.85). Square it (14.8225) and add it to both sides. Add '14.8225' to each side of the equation. -7.7x + 14.8225 + x2 = 0.8 + 14.8225 Reorder the terms: 14.8225 + -7.7x + x2 = 0.8 + 14.8225 Combine like terms: 0.8 + 14.8225 = 15.6225 14.8225 + -7.7x + x2 = 15.6225 Factor a perfect square on the left side: (x + -3.85)(x + -3.85) = 15.6225 Calculate the square root of the right side: 3.952530835 Break this problem into two subproblems by setting (x + -3.85) equal to 3.952530835 and -3.952530835.Subproblem 1
x + -3.85 = 3.952530835 Simplifying x + -3.85 = 3.952530835 Reorder the terms: -3.85 + x = 3.952530835 Solving -3.85 + x = 3.952530835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.85' to each side of the equation. -3.85 + 3.85 + x = 3.952530835 + 3.85 Combine like terms: -3.85 + 3.85 = 0.00 0.00 + x = 3.952530835 + 3.85 x = 3.952530835 + 3.85 Combine like terms: 3.952530835 + 3.85 = 7.802530835 x = 7.802530835 Simplifying x = 7.802530835Subproblem 2
x + -3.85 = -3.952530835 Simplifying x + -3.85 = -3.952530835 Reorder the terms: -3.85 + x = -3.952530835 Solving -3.85 + x = -3.952530835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.85' to each side of the equation. -3.85 + 3.85 + x = -3.952530835 + 3.85 Combine like terms: -3.85 + 3.85 = 0.00 0.00 + x = -3.952530835 + 3.85 x = -3.952530835 + 3.85 Combine like terms: -3.952530835 + 3.85 = -0.102530835 x = -0.102530835 Simplifying x = -0.102530835Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.802530835, -0.102530835}
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