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Simplifying x2 + -6.2x + -42 = 0 Reorder the terms: -42 + -6.2x + x2 = 0 Solving -42 + -6.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -6.2x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -6.2x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -6.2x + x2 = 0 + 42 -6.2x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -6.2x + x2 = 42 The x term is -6.2x. Take half its coefficient (-3.1). Square it (9.61) and add it to both sides. Add '9.61' to each side of the equation. -6.2x + 9.61 + x2 = 42 + 9.61 Reorder the terms: 9.61 + -6.2x + x2 = 42 + 9.61 Combine like terms: 42 + 9.61 = 51.61 9.61 + -6.2x + x2 = 51.61 Factor a perfect square on the left side: (x + -3.1)(x + -3.1) = 51.61 Calculate the square root of the right side: 7.184010022 Break this problem into two subproblems by setting (x + -3.1) equal to 7.184010022 and -7.184010022.Subproblem 1
x + -3.1 = 7.184010022 Simplifying x + -3.1 = 7.184010022 Reorder the terms: -3.1 + x = 7.184010022 Solving -3.1 + x = 7.184010022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.1' to each side of the equation. -3.1 + 3.1 + x = 7.184010022 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + x = 7.184010022 + 3.1 x = 7.184010022 + 3.1 Combine like terms: 7.184010022 + 3.1 = 10.284010022 x = 10.284010022 Simplifying x = 10.284010022Subproblem 2
x + -3.1 = -7.184010022 Simplifying x + -3.1 = -7.184010022 Reorder the terms: -3.1 + x = -7.184010022 Solving -3.1 + x = -7.184010022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.1' to each side of the equation. -3.1 + 3.1 + x = -7.184010022 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + x = -7.184010022 + 3.1 x = -7.184010022 + 3.1 Combine like terms: -7.184010022 + 3.1 = -4.084010022 x = -4.084010022 Simplifying x = -4.084010022Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.284010022, -4.084010022}
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