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Simplifying -16x2 + 56.19x + 2.5 = 0 Reorder the terms: 2.5 + 56.19x + -16x2 = 0 Solving 2.5 + 56.19x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.15625 + -3.511875x + x2 = 0 Move the constant term to the right: Add '0.15625' to each side of the equation. -0.15625 + -3.511875x + 0.15625 + x2 = 0 + 0.15625 Reorder the terms: -0.15625 + 0.15625 + -3.511875x + x2 = 0 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + -3.511875x + x2 = 0 + 0.15625 -3.511875x + x2 = 0 + 0.15625 Combine like terms: 0 + 0.15625 = 0.15625 -3.511875x + x2 = 0.15625 The x term is -3.511875x. Take half its coefficient (-1.7559375). Square it (3.083316504) and add it to both sides. Add '3.083316504' to each side of the equation. -3.511875x + 3.083316504 + x2 = 0.15625 + 3.083316504 Reorder the terms: 3.083316504 + -3.511875x + x2 = 0.15625 + 3.083316504 Combine like terms: 0.15625 + 3.083316504 = 3.239566504 3.083316504 + -3.511875x + x2 = 3.239566504 Factor a perfect square on the left side: (x + -1.7559375)(x + -1.7559375) = 3.239566504 Calculate the square root of the right side: 1.79987958 Break this problem into two subproblems by setting (x + -1.7559375) equal to 1.79987958 and -1.79987958.Subproblem 1
x + -1.7559375 = 1.79987958 Simplifying x + -1.7559375 = 1.79987958 Reorder the terms: -1.7559375 + x = 1.79987958 Solving -1.7559375 + x = 1.79987958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7559375' to each side of the equation. -1.7559375 + 1.7559375 + x = 1.79987958 + 1.7559375 Combine like terms: -1.7559375 + 1.7559375 = 0.0000000 0.0000000 + x = 1.79987958 + 1.7559375 x = 1.79987958 + 1.7559375 Combine like terms: 1.79987958 + 1.7559375 = 3.55581708 x = 3.55581708 Simplifying x = 3.55581708Subproblem 2
x + -1.7559375 = -1.79987958 Simplifying x + -1.7559375 = -1.79987958 Reorder the terms: -1.7559375 + x = -1.79987958 Solving -1.7559375 + x = -1.79987958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7559375' to each side of the equation. -1.7559375 + 1.7559375 + x = -1.79987958 + 1.7559375 Combine like terms: -1.7559375 + 1.7559375 = 0.0000000 0.0000000 + x = -1.79987958 + 1.7559375 x = -1.79987958 + 1.7559375 Combine like terms: -1.79987958 + 1.7559375 = -0.04394208 x = -0.04394208 Simplifying x = -0.04394208Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.55581708, -0.04394208}
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