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Simplifying 4.9x2 + 12x + -26 = 0 Reorder the terms: -26 + 12x + 4.9x2 = 0 Solving -26 + 12x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -5.306122449 + 2.448979592x + x2 = 0 Move the constant term to the right: Add '5.306122449' to each side of the equation. -5.306122449 + 2.448979592x + 5.306122449 + x2 = 0 + 5.306122449 Reorder the terms: -5.306122449 + 5.306122449 + 2.448979592x + x2 = 0 + 5.306122449 Combine like terms: -5.306122449 + 5.306122449 = 0.000000000 0.000000000 + 2.448979592x + x2 = 0 + 5.306122449 2.448979592x + x2 = 0 + 5.306122449 Combine like terms: 0 + 5.306122449 = 5.306122449 2.448979592x + x2 = 5.306122449 The x term is 2.448979592x. Take half its coefficient (1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. 2.448979592x + 1.499375261 + x2 = 5.306122449 + 1.499375261 Reorder the terms: 1.499375261 + 2.448979592x + x2 = 5.306122449 + 1.499375261 Combine like terms: 5.306122449 + 1.499375261 = 6.80549771 1.499375261 + 2.448979592x + x2 = 6.80549771 Factor a perfect square on the left side: (x + 1.224489796)(x + 1.224489796) = 6.80549771 Calculate the square root of the right side: 2.608734887 Break this problem into two subproblems by setting (x + 1.224489796) equal to 2.608734887 and -2.608734887.Subproblem 1
x + 1.224489796 = 2.608734887 Simplifying x + 1.224489796 = 2.608734887 Reorder the terms: 1.224489796 + x = 2.608734887 Solving 1.224489796 + x = 2.608734887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.224489796' to each side of the equation. 1.224489796 + -1.224489796 + x = 2.608734887 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + x = 2.608734887 + -1.224489796 x = 2.608734887 + -1.224489796 Combine like terms: 2.608734887 + -1.224489796 = 1.384245091 x = 1.384245091 Simplifying x = 1.384245091Subproblem 2
x + 1.224489796 = -2.608734887 Simplifying x + 1.224489796 = -2.608734887 Reorder the terms: 1.224489796 + x = -2.608734887 Solving 1.224489796 + x = -2.608734887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.224489796' to each side of the equation. 1.224489796 + -1.224489796 + x = -2.608734887 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + x = -2.608734887 + -1.224489796 x = -2.608734887 + -1.224489796 Combine like terms: -2.608734887 + -1.224489796 = -3.833224683 x = -3.833224683 Simplifying x = -3.833224683Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.384245091, -3.833224683}
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