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Simplifying 5x2 + 19x + -35 = 0 Reorder the terms: -35 + 19x + 5x2 = 0 Solving -35 + 19x + 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'. -7 + 3.8x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 3.8x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 3.8x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3.8x + x2 = 0 + 7 3.8x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 3.8x + x2 = 7 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = 7 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 7 + 3.61 Combine like terms: 7 + 3.61 = 10.61 3.61 + 3.8x + x2 = 10.61 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 10.61 Calculate the square root of the right side: 3.257299495 Break this problem into two subproblems by setting (x + 1.9) equal to 3.257299495 and -3.257299495.Subproblem 1
x + 1.9 = 3.257299495 Simplifying x + 1.9 = 3.257299495 Reorder the terms: 1.9 + x = 3.257299495 Solving 1.9 + x = 3.257299495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 3.257299495 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 3.257299495 + -1.9 x = 3.257299495 + -1.9 Combine like terms: 3.257299495 + -1.9 = 1.357299495 x = 1.357299495 Simplifying x = 1.357299495Subproblem 2
x + 1.9 = -3.257299495 Simplifying x + 1.9 = -3.257299495 Reorder the terms: 1.9 + x = -3.257299495 Solving 1.9 + x = -3.257299495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -3.257299495 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -3.257299495 + -1.9 x = -3.257299495 + -1.9 Combine like terms: -3.257299495 + -1.9 = -5.157299495 x = -5.157299495 Simplifying x = -5.157299495Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.357299495, -5.157299495}
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