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Simplifying (9.81 * 0.5) * x2 + -10x + -3 = 0 Multiply 9.81 * 0.5 (4.905) * x2 + -10x + -3 = 0 Reorder the terms: -3 + -10x + 4.905x2 = 0 Solving -3 + -10x + 4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -0.6116207951 + -2.038735984x + x2 = 0 Move the constant term to the right: Add '0.6116207951' to each side of the equation. -0.6116207951 + -2.038735984x + 0.6116207951 + x2 = 0 + 0.6116207951 Reorder the terms: -0.6116207951 + 0.6116207951 + -2.038735984x + x2 = 0 + 0.6116207951 Combine like terms: -0.6116207951 + 0.6116207951 = 0.0000000000 0.0000000000 + -2.038735984x + x2 = 0 + 0.6116207951 -2.038735984x + x2 = 0 + 0.6116207951 Combine like terms: 0 + 0.6116207951 = 0.6116207951 -2.038735984x + x2 = 0.6116207951 The x term is -2.038735984x. Take half its coefficient (-1.019367992). Square it (1.039111103) and add it to both sides. Add '1.039111103' to each side of the equation. -2.038735984x + 1.039111103 + x2 = 0.6116207951 + 1.039111103 Reorder the terms: 1.039111103 + -2.038735984x + x2 = 0.6116207951 + 1.039111103 Combine like terms: 0.6116207951 + 1.039111103 = 1.6507318981 1.039111103 + -2.038735984x + x2 = 1.6507318981 Factor a perfect square on the left side: (x + -1.019367992)(x + -1.019367992) = 1.6507318981 Calculate the square root of the right side: 1.284808117 Break this problem into two subproblems by setting (x + -1.019367992) equal to 1.284808117 and -1.284808117.Subproblem 1
x + -1.019367992 = 1.284808117 Simplifying x + -1.019367992 = 1.284808117 Reorder the terms: -1.019367992 + x = 1.284808117 Solving -1.019367992 + x = 1.284808117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.019367992' to each side of the equation. -1.019367992 + 1.019367992 + x = 1.284808117 + 1.019367992 Combine like terms: -1.019367992 + 1.019367992 = 0.000000000 0.000000000 + x = 1.284808117 + 1.019367992 x = 1.284808117 + 1.019367992 Combine like terms: 1.284808117 + 1.019367992 = 2.304176109 x = 2.304176109 Simplifying x = 2.304176109Subproblem 2
x + -1.019367992 = -1.284808117 Simplifying x + -1.019367992 = -1.284808117 Reorder the terms: -1.019367992 + x = -1.284808117 Solving -1.019367992 + x = -1.284808117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.019367992' to each side of the equation. -1.019367992 + 1.019367992 + x = -1.284808117 + 1.019367992 Combine like terms: -1.019367992 + 1.019367992 = 0.000000000 0.000000000 + x = -1.284808117 + 1.019367992 x = -1.284808117 + 1.019367992 Combine like terms: -1.284808117 + 1.019367992 = -0.265440125 x = -0.265440125 Simplifying x = -0.265440125Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.304176109, -0.265440125}
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