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Simplifying x2 + 978x + -666 = 0 Reorder the terms: -666 + 978x + x2 = 0 Solving -666 + 978x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '666' to each side of the equation. -666 + 978x + 666 + x2 = 0 + 666 Reorder the terms: -666 + 666 + 978x + x2 = 0 + 666 Combine like terms: -666 + 666 = 0 0 + 978x + x2 = 0 + 666 978x + x2 = 0 + 666 Combine like terms: 0 + 666 = 666 978x + x2 = 666 The x term is 978x. Take half its coefficient (489). Square it (239121) and add it to both sides. Add '239121' to each side of the equation. 978x + 239121 + x2 = 666 + 239121 Reorder the terms: 239121 + 978x + x2 = 666 + 239121 Combine like terms: 666 + 239121 = 239787 239121 + 978x + x2 = 239787 Factor a perfect square on the left side: (x + 489)(x + 489) = 239787 Calculate the square root of the right side: 489.680508087 Break this problem into two subproblems by setting (x + 489) equal to 489.680508087 and -489.680508087.Subproblem 1
x + 489 = 489.680508087 Simplifying x + 489 = 489.680508087 Reorder the terms: 489 + x = 489.680508087 Solving 489 + x = 489.680508087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-489' to each side of the equation. 489 + -489 + x = 489.680508087 + -489 Combine like terms: 489 + -489 = 0 0 + x = 489.680508087 + -489 x = 489.680508087 + -489 Combine like terms: 489.680508087 + -489 = 0.680508087 x = 0.680508087 Simplifying x = 0.680508087Subproblem 2
x + 489 = -489.680508087 Simplifying x + 489 = -489.680508087 Reorder the terms: 489 + x = -489.680508087 Solving 489 + x = -489.680508087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-489' to each side of the equation. 489 + -489 + x = -489.680508087 + -489 Combine like terms: 489 + -489 = 0 0 + x = -489.680508087 + -489 x = -489.680508087 + -489 Combine like terms: -489.680508087 + -489 = -978.680508087 x = -978.680508087 Simplifying x = -978.680508087Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.680508087, -978.680508087}
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