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Simplifying 0 = -0.3x2 + 1.7x + 7 Reorder the terms: 0 = 7 + 1.7x + -0.3x2 Solving 0 = 7 + 1.7x + -0.3x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -1.7x + 0.3x2 = 7 + 1.7x + -0.3x2 + -7 + -1.7x + 0.3x2 Reorder the terms: -7 + -1.7x + 0.3x2 = 7 + -7 + 1.7x + -1.7x + -0.3x2 + 0.3x2 Combine like terms: 7 + -7 = 0 -7 + -1.7x + 0.3x2 = 0 + 1.7x + -1.7x + -0.3x2 + 0.3x2 -7 + -1.7x + 0.3x2 = 1.7x + -1.7x + -0.3x2 + 0.3x2 Combine like terms: 1.7x + -1.7x = 0.0 -7 + -1.7x + 0.3x2 = 0.0 + -0.3x2 + 0.3x2 -7 + -1.7x + 0.3x2 = -0.3x2 + 0.3x2 Combine like terms: -0.3x2 + 0.3x2 = 0.0 -7 + -1.7x + 0.3x2 = 0.0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -23.33333333 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '23.33333333' to each side of the equation. -23.33333333 + -5.666666667x + 23.33333333 + x2 = 0 + 23.33333333 Reorder the terms: -23.33333333 + 23.33333333 + -5.666666667x + x2 = 0 + 23.33333333 Combine like terms: -23.33333333 + 23.33333333 = 0.00000000 0.00000000 + -5.666666667x + x2 = 0 + 23.33333333 -5.666666667x + x2 = 0 + 23.33333333 Combine like terms: 0 + 23.33333333 = 23.33333333 -5.666666667x + x2 = 23.33333333 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = 23.33333333 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 23.33333333 + 8.027777782 Combine like terms: 23.33333333 + 8.027777782 = 31.361111112 8.027777782 + -5.666666667x + x2 = 31.361111112 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 31.361111112 Calculate the square root of the right side: 5.600099206 Break this problem into two subproblems by setting (x + -2.833333334) equal to 5.600099206 and -5.600099206.Subproblem 1
x + -2.833333334 = 5.600099206 Simplifying x + -2.833333334 = 5.600099206 Reorder the terms: -2.833333334 + x = 5.600099206 Solving -2.833333334 + x = 5.600099206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 5.600099206 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 5.600099206 + 2.833333334 x = 5.600099206 + 2.833333334 Combine like terms: 5.600099206 + 2.833333334 = 8.43343254 x = 8.43343254 Simplifying x = 8.43343254Subproblem 2
x + -2.833333334 = -5.600099206 Simplifying x + -2.833333334 = -5.600099206 Reorder the terms: -2.833333334 + x = -5.600099206 Solving -2.833333334 + x = -5.600099206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -5.600099206 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -5.600099206 + 2.833333334 x = -5.600099206 + 2.833333334 Combine like terms: -5.600099206 + 2.833333334 = -2.766765872 x = -2.766765872 Simplifying x = -2.766765872Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.43343254, -2.766765872}
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