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Simplifying 0 = (-4.9) * x2 + 9.62x + 20 Reorder the terms: 0 = 20 + 9.62x + -4.9x2 Solving 0 = 20 + 9.62x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -9.62x + 4.9x2 = 20 + 9.62x + -4.9x2 + -20 + -9.62x + 4.9x2 Reorder the terms: -20 + -9.62x + 4.9x2 = 20 + -20 + 9.62x + -9.62x + -4.9x2 + 4.9x2 Combine like terms: 20 + -20 = 0 -20 + -9.62x + 4.9x2 = 0 + 9.62x + -9.62x + -4.9x2 + 4.9x2 -20 + -9.62x + 4.9x2 = 9.62x + -9.62x + -4.9x2 + 4.9x2 Combine like terms: 9.62x + -9.62x = 0.00 -20 + -9.62x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2 -20 + -9.62x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -20 + -9.62x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -4.081632653 + -1.963265306x + x2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + -1.963265306x + 4.081632653 + x2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + -1.963265306x + x2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + -1.963265306x + x2 = 0 + 4.081632653 -1.963265306x + x2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 -1.963265306x + x2 = 4.081632653 The x term is -1.963265306x. Take half its coefficient (-0.981632653). Square it (0.9636026654) and add it to both sides. Add '0.9636026654' to each side of the equation. -1.963265306x + 0.9636026654 + x2 = 4.081632653 + 0.9636026654 Reorder the terms: 0.9636026654 + -1.963265306x + x2 = 4.081632653 + 0.9636026654 Combine like terms: 4.081632653 + 0.9636026654 = 5.0452353184 0.9636026654 + -1.963265306x + x2 = 5.0452353184 Factor a perfect square on the left side: (x + -0.981632653)(x + -0.981632653) = 5.0452353184 Calculate the square root of the right side: 2.246160128 Break this problem into two subproblems by setting (x + -0.981632653) equal to 2.246160128 and -2.246160128.Subproblem 1
x + -0.981632653 = 2.246160128 Simplifying x + -0.981632653 = 2.246160128 Reorder the terms: -0.981632653 + x = 2.246160128 Solving -0.981632653 + x = 2.246160128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.981632653' to each side of the equation. -0.981632653 + 0.981632653 + x = 2.246160128 + 0.981632653 Combine like terms: -0.981632653 + 0.981632653 = 0.000000000 0.000000000 + x = 2.246160128 + 0.981632653 x = 2.246160128 + 0.981632653 Combine like terms: 2.246160128 + 0.981632653 = 3.227792781 x = 3.227792781 Simplifying x = 3.227792781Subproblem 2
x + -0.981632653 = -2.246160128 Simplifying x + -0.981632653 = -2.246160128 Reorder the terms: -0.981632653 + x = -2.246160128 Solving -0.981632653 + x = -2.246160128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.981632653' to each side of the equation. -0.981632653 + 0.981632653 + x = -2.246160128 + 0.981632653 Combine like terms: -0.981632653 + 0.981632653 = 0.000000000 0.000000000 + x = -2.246160128 + 0.981632653 x = -2.246160128 + 0.981632653 Combine like terms: -2.246160128 + 0.981632653 = -1.264527475 x = -1.264527475 Simplifying x = -1.264527475Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.227792781, -1.264527475}
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