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Simplifying -13x2 + -7x + 14 = 0 Reorder the terms: 14 + -7x + -13x2 = 0 Solving 14 + -7x + -13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -1.076923077 + 0.5384615385x + x2 = 0 Move the constant term to the right: Add '1.076923077' to each side of the equation. -1.076923077 + 0.5384615385x + 1.076923077 + x2 = 0 + 1.076923077 Reorder the terms: -1.076923077 + 1.076923077 + 0.5384615385x + x2 = 0 + 1.076923077 Combine like terms: -1.076923077 + 1.076923077 = 0.000000000 0.000000000 + 0.5384615385x + x2 = 0 + 1.076923077 0.5384615385x + x2 = 0 + 1.076923077 Combine like terms: 0 + 1.076923077 = 1.076923077 0.5384615385x + x2 = 1.076923077 The x term is 0.5384615385x. Take half its coefficient (0.2692307693). Square it (0.07248520714) and add it to both sides. Add '0.07248520714' to each side of the equation. 0.5384615385x + 0.07248520714 + x2 = 1.076923077 + 0.07248520714 Reorder the terms: 0.07248520714 + 0.5384615385x + x2 = 1.076923077 + 0.07248520714 Combine like terms: 1.076923077 + 0.07248520714 = 1.14940828414 0.07248520714 + 0.5384615385x + x2 = 1.14940828414 Factor a perfect square on the left side: (x + 0.2692307693)(x + 0.2692307693) = 1.14940828414 Calculate the square root of the right side: 1.072104605 Break this problem into two subproblems by setting (x + 0.2692307693) equal to 1.072104605 and -1.072104605.Subproblem 1
x + 0.2692307693 = 1.072104605 Simplifying x + 0.2692307693 = 1.072104605 Reorder the terms: 0.2692307693 + x = 1.072104605 Solving 0.2692307693 + x = 1.072104605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = 1.072104605 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = 1.072104605 + -0.2692307693 x = 1.072104605 + -0.2692307693 Combine like terms: 1.072104605 + -0.2692307693 = 0.8028738357 x = 0.8028738357 Simplifying x = 0.8028738357Subproblem 2
x + 0.2692307693 = -1.072104605 Simplifying x + 0.2692307693 = -1.072104605 Reorder the terms: 0.2692307693 + x = -1.072104605 Solving 0.2692307693 + x = -1.072104605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = -1.072104605 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = -1.072104605 + -0.2692307693 x = -1.072104605 + -0.2692307693 Combine like terms: -1.072104605 + -0.2692307693 = -1.3413353743 x = -1.3413353743 Simplifying x = -1.3413353743Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8028738357, -1.3413353743}
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