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Simplifying 42x2 + 31x + -17 = 0 Reorder the terms: -17 + 31x + 42x2 = 0 Solving -17 + 31x + 42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.4047619048 + 0.7380952381x + x2 = 0 Move the constant term to the right: Add '0.4047619048' to each side of the equation. -0.4047619048 + 0.7380952381x + 0.4047619048 + x2 = 0 + 0.4047619048 Reorder the terms: -0.4047619048 + 0.4047619048 + 0.7380952381x + x2 = 0 + 0.4047619048 Combine like terms: -0.4047619048 + 0.4047619048 = 0.0000000000 0.0000000000 + 0.7380952381x + x2 = 0 + 0.4047619048 0.7380952381x + x2 = 0 + 0.4047619048 Combine like terms: 0 + 0.4047619048 = 0.4047619048 0.7380952381x + x2 = 0.4047619048 The x term is 0.7380952381x. Take half its coefficient (0.3690476191). Square it (0.1361961452) and add it to both sides. Add '0.1361961452' to each side of the equation. 0.7380952381x + 0.1361961452 + x2 = 0.4047619048 + 0.1361961452 Reorder the terms: 0.1361961452 + 0.7380952381x + x2 = 0.4047619048 + 0.1361961452 Combine like terms: 0.4047619048 + 0.1361961452 = 0.54095805 0.1361961452 + 0.7380952381x + x2 = 0.54095805 Factor a perfect square on the left side: (x + 0.3690476191)(x + 0.3690476191) = 0.54095805 Calculate the square root of the right side: 0.735498504 Break this problem into two subproblems by setting (x + 0.3690476191) equal to 0.735498504 and -0.735498504.Subproblem 1
x + 0.3690476191 = 0.735498504 Simplifying x + 0.3690476191 = 0.735498504 Reorder the terms: 0.3690476191 + x = 0.735498504 Solving 0.3690476191 + x = 0.735498504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3690476191' to each side of the equation. 0.3690476191 + -0.3690476191 + x = 0.735498504 + -0.3690476191 Combine like terms: 0.3690476191 + -0.3690476191 = 0.0000000000 0.0000000000 + x = 0.735498504 + -0.3690476191 x = 0.735498504 + -0.3690476191 Combine like terms: 0.735498504 + -0.3690476191 = 0.3664508849 x = 0.3664508849 Simplifying x = 0.3664508849Subproblem 2
x + 0.3690476191 = -0.735498504 Simplifying x + 0.3690476191 = -0.735498504 Reorder the terms: 0.3690476191 + x = -0.735498504 Solving 0.3690476191 + x = -0.735498504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3690476191' to each side of the equation. 0.3690476191 + -0.3690476191 + x = -0.735498504 + -0.3690476191 Combine like terms: 0.3690476191 + -0.3690476191 = 0.0000000000 0.0000000000 + x = -0.735498504 + -0.3690476191 x = -0.735498504 + -0.3690476191 Combine like terms: -0.735498504 + -0.3690476191 = -1.1045461231 x = -1.1045461231 Simplifying x = -1.1045461231Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3664508849, -1.1045461231}
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