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Simplifying 5x2 + -34 = x Reorder the terms: -34 + 5x2 = x Solving -34 + 5x2 = x Solving for variable 'x'. Reorder the terms: -34 + -1x + 5x2 = x + -1x Combine like terms: x + -1x = 0 -34 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.8 + -0.2x + x2 = 0 Move the constant term to the right: Add '6.8' to each side of the equation. -6.8 + -0.2x + 6.8 + x2 = 0 + 6.8 Reorder the terms: -6.8 + 6.8 + -0.2x + x2 = 0 + 6.8 Combine like terms: -6.8 + 6.8 = 0.0 0.0 + -0.2x + x2 = 0 + 6.8 -0.2x + x2 = 0 + 6.8 Combine like terms: 0 + 6.8 = 6.8 -0.2x + x2 = 6.8 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 6.8 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 6.8 + 0.01 Combine like terms: 6.8 + 0.01 = 6.81 0.01 + -0.2x + x2 = 6.81 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 6.81 Calculate the square root of the right side: 2.60959767 Break this problem into two subproblems by setting (x + -0.1) equal to 2.60959767 and -2.60959767.Subproblem 1
x + -0.1 = 2.60959767 Simplifying x + -0.1 = 2.60959767 Reorder the terms: -0.1 + x = 2.60959767 Solving -0.1 + x = 2.60959767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 2.60959767 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 2.60959767 + 0.1 x = 2.60959767 + 0.1 Combine like terms: 2.60959767 + 0.1 = 2.70959767 x = 2.70959767 Simplifying x = 2.70959767Subproblem 2
x + -0.1 = -2.60959767 Simplifying x + -0.1 = -2.60959767 Reorder the terms: -0.1 + x = -2.60959767 Solving -0.1 + x = -2.60959767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -2.60959767 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -2.60959767 + 0.1 x = -2.60959767 + 0.1 Combine like terms: -2.60959767 + 0.1 = -2.50959767 x = -2.50959767 Simplifying x = -2.50959767Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.70959767, -2.50959767}
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