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Simplifying 70 = x + 2x2 Solving 70 = x + 2x2 Solving for variable 'x'. Reorder the terms: 70 + -1x + -2x2 = x + -1x + 2x2 + -2x2 Combine like terms: x + -1x = 0 70 + -1x + -2x2 = 0 + 2x2 + -2x2 70 + -1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 70 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -35 + 0.5x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 0.5x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 0.5x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 0.5x + x2 = 0 + 35 0.5x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 0.5x + x2 = 35 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 35 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 35 + 0.0625 Combine like terms: 35 + 0.0625 = 35.0625 0.0625 + 0.5x + x2 = 35.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 35.0625 Calculate the square root of the right side: 5.921359641 Break this problem into two subproblems by setting (x + 0.25) equal to 5.921359641 and -5.921359641.Subproblem 1
x + 0.25 = 5.921359641 Simplifying x + 0.25 = 5.921359641 Reorder the terms: 0.25 + x = 5.921359641 Solving 0.25 + x = 5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 5.921359641 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 5.921359641 + -0.25 x = 5.921359641 + -0.25 Combine like terms: 5.921359641 + -0.25 = 5.671359641 x = 5.671359641 Simplifying x = 5.671359641Subproblem 2
x + 0.25 = -5.921359641 Simplifying x + 0.25 = -5.921359641 Reorder the terms: 0.25 + x = -5.921359641 Solving 0.25 + x = -5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -5.921359641 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -5.921359641 + -0.25 x = -5.921359641 + -0.25 Combine like terms: -5.921359641 + -0.25 = -6.171359641 x = -6.171359641 Simplifying x = -6.171359641Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.671359641, -6.171359641}
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