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Simplifying 3x2 + 5x + 20 = 100 Reorder the terms: 20 + 5x + 3x2 = 100 Solving 20 + 5x + 3x2 = 100 Solving for variable 'x'. Reorder the terms: 20 + -100 + 5x + 3x2 = 100 + -100 Combine like terms: 20 + -100 = -80 -80 + 5x + 3x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -80 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -26.66666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + 1.666666667x + 26.66666667 + x2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + 1.666666667x + x2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + 1.666666667x + x2 = 0 + 26.66666667 1.666666667x + x2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 1.666666667x + x2 = 26.66666667 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 = 26.66666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 26.66666667 + 0.6944444447 Combine like terms: 26.66666667 + 0.6944444447 = 27.3611111147 0.6944444447 + 1.666666667x + x2 = 27.3611111147 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 27.3611111147 Calculate the square root of the right side: 5.230784943 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 5.230784943 and -5.230784943.Subproblem 1
x + 0.8333333335 = 5.230784943 Simplifying x + 0.8333333335 = 5.230784943 Reorder the terms: 0.8333333335 + x = 5.230784943 Solving 0.8333333335 + x = 5.230784943 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 = 5.230784943 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 5.230784943 + -0.8333333335 x = 5.230784943 + -0.8333333335 Combine like terms: 5.230784943 + -0.8333333335 = 4.3974516095 x = 4.3974516095 Simplifying x = 4.3974516095Subproblem 2
x + 0.8333333335 = -5.230784943 Simplifying x + 0.8333333335 = -5.230784943 Reorder the terms: 0.8333333335 + x = -5.230784943 Solving 0.8333333335 + x = -5.230784943 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 = -5.230784943 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -5.230784943 + -0.8333333335 x = -5.230784943 + -0.8333333335 Combine like terms: -5.230784943 + -0.8333333335 = -6.0641182765 x = -6.0641182765 Simplifying x = -6.0641182765Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.3974516095, -6.0641182765}
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