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Simplifying 2x2 + 3x + -140 = 0 Reorder the terms: -140 + 3x + 2x2 = 0 Solving -140 + 3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -70 + 1.5x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + 1.5x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 1.5x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 1.5x + x2 = 0 + 70 1.5x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 1.5x + x2 = 70 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 70 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 70 + 0.5625 Combine like terms: 70 + 0.5625 = 70.5625 0.5625 + 1.5x + x2 = 70.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 70.5625 Calculate the square root of the right side: 8.400148808 Break this problem into two subproblems by setting (x + 0.75) equal to 8.400148808 and -8.400148808.Subproblem 1
x + 0.75 = 8.400148808 Simplifying x + 0.75 = 8.400148808 Reorder the terms: 0.75 + x = 8.400148808 Solving 0.75 + x = 8.400148808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 8.400148808 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 8.400148808 + -0.75 x = 8.400148808 + -0.75 Combine like terms: 8.400148808 + -0.75 = 7.650148808 x = 7.650148808 Simplifying x = 7.650148808Subproblem 2
x + 0.75 = -8.400148808 Simplifying x + 0.75 = -8.400148808 Reorder the terms: 0.75 + x = -8.400148808 Solving 0.75 + x = -8.400148808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -8.400148808 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -8.400148808 + -0.75 x = -8.400148808 + -0.75 Combine like terms: -8.400148808 + -0.75 = -9.150148808 x = -9.150148808 Simplifying x = -9.150148808Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.650148808, -9.150148808}
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