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Simplifying 5x2 + -34x + -343 = 0 Reorder the terms: -343 + -34x + 5x2 = 0 Solving -343 + -34x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -68.6 + -6.8x + x2 = 0 Move the constant term to the right: Add '68.6' to each side of the equation. -68.6 + -6.8x + 68.6 + x2 = 0 + 68.6 Reorder the terms: -68.6 + 68.6 + -6.8x + x2 = 0 + 68.6 Combine like terms: -68.6 + 68.6 = 0.0 0.0 + -6.8x + x2 = 0 + 68.6 -6.8x + x2 = 0 + 68.6 Combine like terms: 0 + 68.6 = 68.6 -6.8x + x2 = 68.6 The x term is -6.8x. Take half its coefficient (-3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. -6.8x + 11.56 + x2 = 68.6 + 11.56 Reorder the terms: 11.56 + -6.8x + x2 = 68.6 + 11.56 Combine like terms: 68.6 + 11.56 = 80.16 11.56 + -6.8x + x2 = 80.16 Factor a perfect square on the left side: (x + -3.4)(x + -3.4) = 80.16 Calculate the square root of the right side: 8.953211714 Break this problem into two subproblems by setting (x + -3.4) equal to 8.953211714 and -8.953211714.Subproblem 1
x + -3.4 = 8.953211714 Simplifying x + -3.4 = 8.953211714 Reorder the terms: -3.4 + x = 8.953211714 Solving -3.4 + x = 8.953211714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = 8.953211714 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = 8.953211714 + 3.4 x = 8.953211714 + 3.4 Combine like terms: 8.953211714 + 3.4 = 12.353211714 x = 12.353211714 Simplifying x = 12.353211714Subproblem 2
x + -3.4 = -8.953211714 Simplifying x + -3.4 = -8.953211714 Reorder the terms: -3.4 + x = -8.953211714 Solving -3.4 + x = -8.953211714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = -8.953211714 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = -8.953211714 + 3.4 x = -8.953211714 + 3.4 Combine like terms: -8.953211714 + 3.4 = -5.553211714 x = -5.553211714 Simplifying x = -5.553211714Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.353211714, -5.553211714}
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