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Simplifying 15x2 + 8x + 3 = 42 Reorder the terms: 3 + 8x + 15x2 = 42 Solving 3 + 8x + 15x2 = 42 Solving for variable 'x'. Reorder the terms: 3 + -42 + 8x + 15x2 = 42 + -42 Combine like terms: 3 + -42 = -39 -39 + 8x + 15x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -39 + 8x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -2.6 + 0.5333333333x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 0.5333333333x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 0.5333333333x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 0.5333333333x + x2 = 0 + 2.6 0.5333333333x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 0.5333333333x + x2 = 2.6 The x term is 0.5333333333x. Take half its coefficient (0.2666666667). Square it (0.07111111113) and add it to both sides. Add '0.07111111113' to each side of the equation. 0.5333333333x + 0.07111111113 + x2 = 2.6 + 0.07111111113 Reorder the terms: 0.07111111113 + 0.5333333333x + x2 = 2.6 + 0.07111111113 Combine like terms: 2.6 + 0.07111111113 = 2.67111111113 0.07111111113 + 0.5333333333x + x2 = 2.67111111113 Factor a perfect square on the left side: (x + 0.2666666667)(x + 0.2666666667) = 2.67111111113 Calculate the square root of the right side: 1.634353423 Break this problem into two subproblems by setting (x + 0.2666666667) equal to 1.634353423 and -1.634353423.Subproblem 1
x + 0.2666666667 = 1.634353423 Simplifying x + 0.2666666667 = 1.634353423 Reorder the terms: 0.2666666667 + x = 1.634353423 Solving 0.2666666667 + x = 1.634353423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2666666667' to each side of the equation. 0.2666666667 + -0.2666666667 + x = 1.634353423 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + x = 1.634353423 + -0.2666666667 x = 1.634353423 + -0.2666666667 Combine like terms: 1.634353423 + -0.2666666667 = 1.3676867563 x = 1.3676867563 Simplifying x = 1.3676867563Subproblem 2
x + 0.2666666667 = -1.634353423 Simplifying x + 0.2666666667 = -1.634353423 Reorder the terms: 0.2666666667 + x = -1.634353423 Solving 0.2666666667 + x = -1.634353423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2666666667' to each side of the equation. 0.2666666667 + -0.2666666667 + x = -1.634353423 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + x = -1.634353423 + -0.2666666667 x = -1.634353423 + -0.2666666667 Combine like terms: -1.634353423 + -0.2666666667 = -1.9010200897 x = -1.9010200897 Simplifying x = -1.9010200897Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3676867563, -1.9010200897}
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