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Simplifying 5x2 + -60 = x Reorder the terms: -60 + 5x2 = x Solving -60 + 5x2 = x Solving for variable 'x'. Reorder the terms: -60 + -1x + 5x2 = x + -1x Combine like terms: x + -1x = 0 -60 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12 + -0.2x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -0.2x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -0.2x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -0.2x + x2 = 0 + 12 -0.2x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -0.2x + x2 = 12 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 = 12 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 12 + 0.01 Combine like terms: 12 + 0.01 = 12.01 0.01 + -0.2x + x2 = 12.01 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 12.01 Calculate the square root of the right side: 3.46554469 Break this problem into two subproblems by setting (x + -0.1) equal to 3.46554469 and -3.46554469.Subproblem 1
x + -0.1 = 3.46554469 Simplifying x + -0.1 = 3.46554469 Reorder the terms: -0.1 + x = 3.46554469 Solving -0.1 + x = 3.46554469 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 = 3.46554469 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 3.46554469 + 0.1 x = 3.46554469 + 0.1 Combine like terms: 3.46554469 + 0.1 = 3.56554469 x = 3.56554469 Simplifying x = 3.56554469Subproblem 2
x + -0.1 = -3.46554469 Simplifying x + -0.1 = -3.46554469 Reorder the terms: -0.1 + x = -3.46554469 Solving -0.1 + x = -3.46554469 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 = -3.46554469 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -3.46554469 + 0.1 x = -3.46554469 + 0.1 Combine like terms: -3.46554469 + 0.1 = -3.36554469 x = -3.36554469 Simplifying x = -3.36554469Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.56554469, -3.36554469}
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