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Simplifying 0 = -16x2 + 19.5x + 6.5 Reorder the terms: 0 = 6.5 + 19.5x + -16x2 Solving 0 = 6.5 + 19.5x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -6.5 = -6.5 -6.5 + -19.5x + 16x2 = 6.5 + 19.5x + -16x2 + -6.5 + -19.5x + 16x2 Reorder the terms: -6.5 + -19.5x + 16x2 = 6.5 + -6.5 + 19.5x + -19.5x + -16x2 + 16x2 Combine like terms: 6.5 + -6.5 = 0.0 -6.5 + -19.5x + 16x2 = 0.0 + 19.5x + -19.5x + -16x2 + 16x2 -6.5 + -19.5x + 16x2 = 19.5x + -19.5x + -16x2 + 16x2 Combine like terms: 19.5x + -19.5x = 0.0 -6.5 + -19.5x + 16x2 = 0.0 + -16x2 + 16x2 -6.5 + -19.5x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -6.5 + -19.5x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.40625 + -1.21875x + x2 = 0 Move the constant term to the right: Add '0.40625' to each side of the equation. -0.40625 + -1.21875x + 0.40625 + x2 = 0 + 0.40625 Reorder the terms: -0.40625 + 0.40625 + -1.21875x + x2 = 0 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + -1.21875x + x2 = 0 + 0.40625 -1.21875x + x2 = 0 + 0.40625 Combine like terms: 0 + 0.40625 = 0.40625 -1.21875x + x2 = 0.40625 The x term is -1.21875x. Take half its coefficient (-0.609375). Square it (0.3713378906) and add it to both sides. Add '0.3713378906' to each side of the equation. -1.21875x + 0.3713378906 + x2 = 0.40625 + 0.3713378906 Reorder the terms: 0.3713378906 + -1.21875x + x2 = 0.40625 + 0.3713378906 Combine like terms: 0.40625 + 0.3713378906 = 0.7775878906 0.3713378906 + -1.21875x + x2 = 0.7775878906 Factor a perfect square on the left side: (x + -0.609375)(x + -0.609375) = 0.7775878906 Calculate the square root of the right side: 0.881809441 Break this problem into two subproblems by setting (x + -0.609375) equal to 0.881809441 and -0.881809441.Subproblem 1
x + -0.609375 = 0.881809441 Simplifying x + -0.609375 = 0.881809441 Reorder the terms: -0.609375 + x = 0.881809441 Solving -0.609375 + x = 0.881809441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.609375' to each side of the equation. -0.609375 + 0.609375 + x = 0.881809441 + 0.609375 Combine like terms: -0.609375 + 0.609375 = 0.000000 0.000000 + x = 0.881809441 + 0.609375 x = 0.881809441 + 0.609375 Combine like terms: 0.881809441 + 0.609375 = 1.491184441 x = 1.491184441 Simplifying x = 1.491184441Subproblem 2
x + -0.609375 = -0.881809441 Simplifying x + -0.609375 = -0.881809441 Reorder the terms: -0.609375 + x = -0.881809441 Solving -0.609375 + x = -0.881809441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.609375' to each side of the equation. -0.609375 + 0.609375 + x = -0.881809441 + 0.609375 Combine like terms: -0.609375 + 0.609375 = 0.000000 0.000000 + x = -0.881809441 + 0.609375 x = -0.881809441 + 0.609375 Combine like terms: -0.881809441 + 0.609375 = -0.272434441 x = -0.272434441 Simplifying x = -0.272434441Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.491184441, -0.272434441}
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