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Simplifying 5x2 + 34x + -10 = 0 Reorder the terms: -10 + 34x + 5x2 = 0 Solving -10 + 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'. -2 + 6.8x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 6.8x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 6.8x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6.8x + x2 = 0 + 2 6.8x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 6.8x + x2 = 2 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 = 2 + 11.56 Reorder the terms: 11.56 + 6.8x + x2 = 2 + 11.56 Combine like terms: 2 + 11.56 = 13.56 11.56 + 6.8x + x2 = 13.56 Factor a perfect square on the left side: (x + 3.4)(x + 3.4) = 13.56 Calculate the square root of the right side: 3.682390528 Break this problem into two subproblems by setting (x + 3.4) equal to 3.682390528 and -3.682390528.Subproblem 1
x + 3.4 = 3.682390528 Simplifying x + 3.4 = 3.682390528 Reorder the terms: 3.4 + x = 3.682390528 Solving 3.4 + x = 3.682390528 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 = 3.682390528 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = 3.682390528 + -3.4 x = 3.682390528 + -3.4 Combine like terms: 3.682390528 + -3.4 = 0.282390528 x = 0.282390528 Simplifying x = 0.282390528Subproblem 2
x + 3.4 = -3.682390528 Simplifying x + 3.4 = -3.682390528 Reorder the terms: 3.4 + x = -3.682390528 Solving 3.4 + x = -3.682390528 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 = -3.682390528 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = -3.682390528 + -3.4 x = -3.682390528 + -3.4 Combine like terms: -3.682390528 + -3.4 = -7.082390528 x = -7.082390528 Simplifying x = -7.082390528Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.282390528, -7.082390528}
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