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Simplifying 0 = 1.4x2 + -1x + -30 Reorder the terms: 0 = -30 + -1x + 1.4x2 Solving 0 = -30 + -1x + 1.4x2 Solving for variable 'x'. Combine like terms: 0 + 30 = 30 30 + x + -1.4x2 = -30 + -1x + 1.4x2 + 30 + x + -1.4x2 Reorder the terms: 30 + x + -1.4x2 = -30 + 30 + -1x + x + 1.4x2 + -1.4x2 Combine like terms: -30 + 30 = 0 30 + x + -1.4x2 = 0 + -1x + x + 1.4x2 + -1.4x2 30 + x + -1.4x2 = -1x + x + 1.4x2 + -1.4x2 Combine like terms: -1x + x = 0 30 + x + -1.4x2 = 0 + 1.4x2 + -1.4x2 30 + x + -1.4x2 = 1.4x2 + -1.4x2 Combine like terms: 1.4x2 + -1.4x2 = 0.0 30 + x + -1.4x2 = 0.0 Begin completing the square. Divide all terms by -1.4 the coefficient of the squared term: Divide each side by '-1.4'. -21.42857143 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '21.42857143' to each side of the equation. -21.42857143 + -0.7142857143x + 21.42857143 + x2 = 0 + 21.42857143 Reorder the terms: -21.42857143 + 21.42857143 + -0.7142857143x + x2 = 0 + 21.42857143 Combine like terms: -21.42857143 + 21.42857143 = 0.00000000 0.00000000 + -0.7142857143x + x2 = 0 + 21.42857143 -0.7142857143x + x2 = 0 + 21.42857143 Combine like terms: 0 + 21.42857143 = 21.42857143 -0.7142857143x + x2 = 21.42857143 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.7142857143x + 0.25 + x2 = 21.42857143 + 0.25 Reorder the terms: 0.25 + -0.7142857143x + x2 = 21.42857143 + 0.25 Combine like terms: 21.42857143 + 0.25 = 21.67857143 0.25 + -0.7142857143x + x2 = 21.67857143 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 21.67857143 Calculate the square root of the right side: 4.656025282 Break this problem into two subproblems by setting (x + 0.5) equal to 4.656025282 and -4.656025282.Subproblem 1
x + 0.5 = 4.656025282 Simplifying x + 0.5 = 4.656025282 Reorder the terms: 0.5 + x = 4.656025282 Solving 0.5 + x = 4.656025282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.656025282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.656025282 + -0.5 x = 4.656025282 + -0.5 Combine like terms: 4.656025282 + -0.5 = 4.156025282 x = 4.156025282 Simplifying x = 4.156025282Subproblem 2
x + 0.5 = -4.656025282 Simplifying x + 0.5 = -4.656025282 Reorder the terms: 0.5 + x = -4.656025282 Solving 0.5 + x = -4.656025282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.656025282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.656025282 + -0.5 x = -4.656025282 + -0.5 Combine like terms: -4.656025282 + -0.5 = -5.156025282 x = -5.156025282 Simplifying x = -5.156025282Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.156025282, -5.156025282}
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