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Simplifying 3x2 + 5x + -297 = 0 Reorder the terms: -297 + 5x + 3x2 = 0 Solving -297 + 5x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -99 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '99' to each side of the equation. -99 + 1.666666667x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + 1.666666667x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 1.666666667x + x2 = 0 + 99 1.666666667x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 1.666666667x + x2 = 99 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 99 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 99 + 0.6944444447 Combine like terms: 99 + 0.6944444447 = 99.6944444447 0.6944444447 + 1.666666667x + x2 = 99.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 99.6944444447 Calculate the square root of the right side: 9.984710534 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 9.984710534 and -9.984710534.Subproblem 1
x + 0.8333333335 = 9.984710534 Simplifying x + 0.8333333335 = 9.984710534 Reorder the terms: 0.8333333335 + x = 9.984710534 Solving 0.8333333335 + x = 9.984710534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 9.984710534 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 9.984710534 + -0.8333333335 x = 9.984710534 + -0.8333333335 Combine like terms: 9.984710534 + -0.8333333335 = 9.1513772005 x = 9.1513772005 Simplifying x = 9.1513772005Subproblem 2
x + 0.8333333335 = -9.984710534 Simplifying x + 0.8333333335 = -9.984710534 Reorder the terms: 0.8333333335 + x = -9.984710534 Solving 0.8333333335 + x = -9.984710534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -9.984710534 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -9.984710534 + -0.8333333335 x = -9.984710534 + -0.8333333335 Combine like terms: -9.984710534 + -0.8333333335 = -10.8180438675 x = -10.8180438675 Simplifying x = -10.8180438675Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.1513772005, -10.8180438675}
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