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Simplifying 3x2 + 5x = 291 Reorder the terms: 5x + 3x2 = 291 Solving 5x + 3x2 = 291 Solving for variable 'x'. Reorder the terms: -291 + 5x + 3x2 = 291 + -291 Combine like terms: 291 + -291 = 0 -291 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -97 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '97' to each side of the equation. -97 + 1.666666667x + 97 + x2 = 0 + 97 Reorder the terms: -97 + 97 + 1.666666667x + x2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + 1.666666667x + x2 = 0 + 97 1.666666667x + x2 = 0 + 97 Combine like terms: 0 + 97 = 97 1.666666667x + x2 = 97 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 = 97 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 97 + 0.6944444447 Combine like terms: 97 + 0.6944444447 = 97.6944444447 0.6944444447 + 1.666666667x + x2 = 97.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 97.6944444447 Calculate the square root of the right side: 9.884050002 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 9.884050002 and -9.884050002.Subproblem 1
x + 0.8333333335 = 9.884050002 Simplifying x + 0.8333333335 = 9.884050002 Reorder the terms: 0.8333333335 + x = 9.884050002 Solving 0.8333333335 + x = 9.884050002 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 = 9.884050002 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 9.884050002 + -0.8333333335 x = 9.884050002 + -0.8333333335 Combine like terms: 9.884050002 + -0.8333333335 = 9.0507166685 x = 9.0507166685 Simplifying x = 9.0507166685Subproblem 2
x + 0.8333333335 = -9.884050002 Simplifying x + 0.8333333335 = -9.884050002 Reorder the terms: 0.8333333335 + x = -9.884050002 Solving 0.8333333335 + x = -9.884050002 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 = -9.884050002 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -9.884050002 + -0.8333333335 x = -9.884050002 + -0.8333333335 Combine like terms: -9.884050002 + -0.8333333335 = -10.7173833355 x = -10.7173833355 Simplifying x = -10.7173833355Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.0507166685, -10.7173833355}
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