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Simplifying 10.4 = 0.99x2 + -3.54x + 7 Reorder the terms: 10.4 = 7 + -3.54x + 0.99x2 Solving 10.4 = 7 + -3.54x + 0.99x2 Solving for variable 'x'. Combine like terms: 10.4 + -7 = 3.4 3.4 + 3.54x + -0.99x2 = 7 + -3.54x + 0.99x2 + -7 + 3.54x + -0.99x2 Reorder the terms: 3.4 + 3.54x + -0.99x2 = 7 + -7 + -3.54x + 3.54x + 0.99x2 + -0.99x2 Combine like terms: 7 + -7 = 0 3.4 + 3.54x + -0.99x2 = 0 + -3.54x + 3.54x + 0.99x2 + -0.99x2 3.4 + 3.54x + -0.99x2 = -3.54x + 3.54x + 0.99x2 + -0.99x2 Combine like terms: -3.54x + 3.54x = 0.00 3.4 + 3.54x + -0.99x2 = 0.00 + 0.99x2 + -0.99x2 3.4 + 3.54x + -0.99x2 = 0.99x2 + -0.99x2 Combine like terms: 0.99x2 + -0.99x2 = 0.00 3.4 + 3.54x + -0.99x2 = 0.00 Begin completing the square. Divide all terms by -0.99 the coefficient of the squared term: Divide each side by '-0.99'. -3.434343434 + -3.575757576x + x2 = 0 Move the constant term to the right: Add '3.434343434' to each side of the equation. -3.434343434 + -3.575757576x + 3.434343434 + x2 = 0 + 3.434343434 Reorder the terms: -3.434343434 + 3.434343434 + -3.575757576x + x2 = 0 + 3.434343434 Combine like terms: -3.434343434 + 3.434343434 = 0.000000000 0.000000000 + -3.575757576x + x2 = 0 + 3.434343434 -3.575757576x + x2 = 0 + 3.434343434 Combine like terms: 0 + 3.434343434 = 3.434343434 -3.575757576x + x2 = 3.434343434 The x term is -3.575757576x. Take half its coefficient (-1.787878788). Square it (3.196510561) and add it to both sides. Add '3.196510561' to each side of the equation. -3.575757576x + 3.196510561 + x2 = 3.434343434 + 3.196510561 Reorder the terms: 3.196510561 + -3.575757576x + x2 = 3.434343434 + 3.196510561 Combine like terms: 3.434343434 + 3.196510561 = 6.630853995 3.196510561 + -3.575757576x + x2 = 6.630853995 Factor a perfect square on the left side: (x + -1.787878788)(x + -1.787878788) = 6.630853995 Calculate the square root of the right side: 2.575044465 Break this problem into two subproblems by setting (x + -1.787878788) equal to 2.575044465 and -2.575044465.Subproblem 1
x + -1.787878788 = 2.575044465 Simplifying x + -1.787878788 = 2.575044465 Reorder the terms: -1.787878788 + x = 2.575044465 Solving -1.787878788 + x = 2.575044465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.787878788' to each side of the equation. -1.787878788 + 1.787878788 + x = 2.575044465 + 1.787878788 Combine like terms: -1.787878788 + 1.787878788 = 0.000000000 0.000000000 + x = 2.575044465 + 1.787878788 x = 2.575044465 + 1.787878788 Combine like terms: 2.575044465 + 1.787878788 = 4.362923253 x = 4.362923253 Simplifying x = 4.362923253Subproblem 2
x + -1.787878788 = -2.575044465 Simplifying x + -1.787878788 = -2.575044465 Reorder the terms: -1.787878788 + x = -2.575044465 Solving -1.787878788 + x = -2.575044465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.787878788' to each side of the equation. -1.787878788 + 1.787878788 + x = -2.575044465 + 1.787878788 Combine like terms: -1.787878788 + 1.787878788 = 0.000000000 0.000000000 + x = -2.575044465 + 1.787878788 x = -2.575044465 + 1.787878788 Combine like terms: -2.575044465 + 1.787878788 = -0.787165677 x = -0.787165677 Simplifying x = -0.787165677Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.362923253, -0.787165677}
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