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Simplifying x2 + 5x = 7x + 70 Reorder the terms: 5x + x2 = 7x + 70 Reorder the terms: 5x + x2 = 70 + 7x Solving 5x + x2 = 70 + 7x Solving for variable 'x'. Reorder the terms: -70 + 5x + -7x + x2 = 70 + 7x + -70 + -7x Combine like terms: 5x + -7x = -2x -70 + -2x + x2 = 70 + 7x + -70 + -7x Reorder the terms: -70 + -2x + x2 = 70 + -70 + 7x + -7x Combine like terms: 70 + -70 = 0 -70 + -2x + x2 = 0 + 7x + -7x -70 + -2x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -70 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -2x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + -2x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -2x + x2 = 0 + 70 -2x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -2x + x2 = 70 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 70 + 1 Reorder the terms: 1 + -2x + x2 = 70 + 1 Combine like terms: 70 + 1 = 71 1 + -2x + x2 = 71 Factor a perfect square on the left side: (x + -1)(x + -1) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + -1) equal to 8.426149773 and -8.426149773.Subproblem 1
x + -1 = 8.426149773 Simplifying x + -1 = 8.426149773 Reorder the terms: -1 + x = 8.426149773 Solving -1 + x = 8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 8.426149773 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.426149773 + 1 x = 8.426149773 + 1 Combine like terms: 8.426149773 + 1 = 9.426149773 x = 9.426149773 Simplifying x = 9.426149773Subproblem 2
x + -1 = -8.426149773 Simplifying x + -1 = -8.426149773 Reorder the terms: -1 + x = -8.426149773 Solving -1 + x = -8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -8.426149773 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.426149773 + 1 x = -8.426149773 + 1 Combine like terms: -8.426149773 + 1 = -7.426149773 x = -7.426149773 Simplifying x = -7.426149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.426149773, -7.426149773}
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