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Simplifying 276 = 17x2 + -51.1x + 305.4 Reorder the terms: 276 = 305.4 + -51.1x + 17x2 Solving 276 = 305.4 + -51.1x + 17x2 Solving for variable 'x'. Combine like terms: 276 + -305.4 = -29.4 -29.4 + 51.1x + -17x2 = 305.4 + -51.1x + 17x2 + -305.4 + 51.1x + -17x2 Reorder the terms: -29.4 + 51.1x + -17x2 = 305.4 + -305.4 + -51.1x + 51.1x + 17x2 + -17x2 Combine like terms: 305.4 + -305.4 = 0.0 -29.4 + 51.1x + -17x2 = 0.0 + -51.1x + 51.1x + 17x2 + -17x2 -29.4 + 51.1x + -17x2 = -51.1x + 51.1x + 17x2 + -17x2 Combine like terms: -51.1x + 51.1x = 0.0 -29.4 + 51.1x + -17x2 = 0.0 + 17x2 + -17x2 -29.4 + 51.1x + -17x2 = 17x2 + -17x2 Combine like terms: 17x2 + -17x2 = 0 -29.4 + 51.1x + -17x2 = 0 Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. 1.729411765 + -3.005882353x + x2 = 0 Move the constant term to the right: Add '-1.729411765' to each side of the equation. 1.729411765 + -3.005882353x + -1.729411765 + x2 = 0 + -1.729411765 Reorder the terms: 1.729411765 + -1.729411765 + -3.005882353x + x2 = 0 + -1.729411765 Combine like terms: 1.729411765 + -1.729411765 = 0.000000000 0.000000000 + -3.005882353x + x2 = 0 + -1.729411765 -3.005882353x + x2 = 0 + -1.729411765 Combine like terms: 0 + -1.729411765 = -1.729411765 -3.005882353x + x2 = -1.729411765 The x term is -3.005882353x. Take half its coefficient (-1.502941177). Square it (2.258832182) and add it to both sides. Add '2.258832182' to each side of the equation. -3.005882353x + 2.258832182 + x2 = -1.729411765 + 2.258832182 Reorder the terms: 2.258832182 + -3.005882353x + x2 = -1.729411765 + 2.258832182 Combine like terms: -1.729411765 + 2.258832182 = 0.529420417 2.258832182 + -3.005882353x + x2 = 0.529420417 Factor a perfect square on the left side: (x + -1.502941177)(x + -1.502941177) = 0.529420417 Calculate the square root of the right side: 0.727612821 Break this problem into two subproblems by setting (x + -1.502941177) equal to 0.727612821 and -0.727612821.Subproblem 1
x + -1.502941177 = 0.727612821 Simplifying x + -1.502941177 = 0.727612821 Reorder the terms: -1.502941177 + x = 0.727612821 Solving -1.502941177 + x = 0.727612821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.502941177' to each side of the equation. -1.502941177 + 1.502941177 + x = 0.727612821 + 1.502941177 Combine like terms: -1.502941177 + 1.502941177 = 0.000000000 0.000000000 + x = 0.727612821 + 1.502941177 x = 0.727612821 + 1.502941177 Combine like terms: 0.727612821 + 1.502941177 = 2.230553998 x = 2.230553998 Simplifying x = 2.230553998Subproblem 2
x + -1.502941177 = -0.727612821 Simplifying x + -1.502941177 = -0.727612821 Reorder the terms: -1.502941177 + x = -0.727612821 Solving -1.502941177 + x = -0.727612821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.502941177' to each side of the equation. -1.502941177 + 1.502941177 + x = -0.727612821 + 1.502941177 Combine like terms: -1.502941177 + 1.502941177 = 0.000000000 0.000000000 + x = -0.727612821 + 1.502941177 x = -0.727612821 + 1.502941177 Combine like terms: -0.727612821 + 1.502941177 = 0.775328356 x = 0.775328356 Simplifying x = 0.775328356Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.230553998, 0.775328356}
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