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Simplifying 0 = 2.15 + 9.6x + (0.5)(-9.81)(x2) Multiply 0.5 * -9.81 0 = 2.15 + 9.6x + -4.905x2 Solving 0 = 2.15 + 9.6x + -4.905x2 Solving for variable 'x'. Combine like terms: 0 + -2.15 = -2.15 -2.15 + -9.6x + 4.905x2 = 2.15 + 9.6x + -4.905x2 + -2.15 + -9.6x + 4.905x2 Reorder the terms: -2.15 + -9.6x + 4.905x2 = 2.15 + -2.15 + 9.6x + -9.6x + -4.905x2 + 4.905x2 Combine like terms: 2.15 + -2.15 = 0.00 -2.15 + -9.6x + 4.905x2 = 0.00 + 9.6x + -9.6x + -4.905x2 + 4.905x2 -2.15 + -9.6x + 4.905x2 = 9.6x + -9.6x + -4.905x2 + 4.905x2 Combine like terms: 9.6x + -9.6x = 0.0 -2.15 + -9.6x + 4.905x2 = 0.0 + -4.905x2 + 4.905x2 -2.15 + -9.6x + 4.905x2 = -4.905x2 + 4.905x2 Combine like terms: -4.905x2 + 4.905x2 = 0.000 -2.15 + -9.6x + 4.905x2 = 0.000 Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -0.4383282365 + -1.957186544x + x2 = 0 Move the constant term to the right: Add '0.4383282365' to each side of the equation. -0.4383282365 + -1.957186544x + 0.4383282365 + x2 = 0 + 0.4383282365 Reorder the terms: -0.4383282365 + 0.4383282365 + -1.957186544x + x2 = 0 + 0.4383282365 Combine like terms: -0.4383282365 + 0.4383282365 = 0.0000000000 0.0000000000 + -1.957186544x + x2 = 0 + 0.4383282365 -1.957186544x + x2 = 0 + 0.4383282365 Combine like terms: 0 + 0.4383282365 = 0.4383282365 -1.957186544x + x2 = 0.4383282365 The x term is -1.957186544x. Take half its coefficient (-0.978593272). Square it (0.9576447920) and add it to both sides. Add '0.9576447920' to each side of the equation. -1.957186544x + 0.9576447920 + x2 = 0.4383282365 + 0.9576447920 Reorder the terms: 0.9576447920 + -1.957186544x + x2 = 0.4383282365 + 0.9576447920 Combine like terms: 0.4383282365 + 0.9576447920 = 1.3959730285 0.9576447920 + -1.957186544x + x2 = 1.3959730285 Factor a perfect square on the left side: (x + -0.978593272)(x + -0.978593272) = 1.3959730285 Calculate the square root of the right side: 1.181513025 Break this problem into two subproblems by setting (x + -0.978593272) equal to 1.181513025 and -1.181513025.Subproblem 1
x + -0.978593272 = 1.181513025 Simplifying x + -0.978593272 = 1.181513025 Reorder the terms: -0.978593272 + x = 1.181513025 Solving -0.978593272 + x = 1.181513025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.978593272' to each side of the equation. -0.978593272 + 0.978593272 + x = 1.181513025 + 0.978593272 Combine like terms: -0.978593272 + 0.978593272 = 0.000000000 0.000000000 + x = 1.181513025 + 0.978593272 x = 1.181513025 + 0.978593272 Combine like terms: 1.181513025 + 0.978593272 = 2.160106297 x = 2.160106297 Simplifying x = 2.160106297Subproblem 2
x + -0.978593272 = -1.181513025 Simplifying x + -0.978593272 = -1.181513025 Reorder the terms: -0.978593272 + x = -1.181513025 Solving -0.978593272 + x = -1.181513025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.978593272' to each side of the equation. -0.978593272 + 0.978593272 + x = -1.181513025 + 0.978593272 Combine like terms: -0.978593272 + 0.978593272 = 0.000000000 0.000000000 + x = -1.181513025 + 0.978593272 x = -1.181513025 + 0.978593272 Combine like terms: -1.181513025 + 0.978593272 = -0.202919753 x = -0.202919753 Simplifying x = -0.202919753Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.160106297, -0.202919753}
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