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Simplifying 21.3 = -4.9x2 + 21.3x Reorder the terms: 21.3 = 21.3x + -4.9x2 Solving 21.3 = 21.3x + -4.9x2 Solving for variable 'x'. Reorder the terms: 21.3 + -21.3x + 4.9x2 = 21.3x + -21.3x + -4.9x2 + 4.9x2 Combine like terms: 21.3x + -21.3x = 0.0 21.3 + -21.3x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 21.3 + -21.3x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 21.3 + -21.3x + 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'. 4.346938776 + -4.346938776x + x2 = 0 Move the constant term to the right: Add '-4.346938776' to each side of the equation. 4.346938776 + -4.346938776x + -4.346938776 + x2 = 0 + -4.346938776 Reorder the terms: 4.346938776 + -4.346938776 + -4.346938776x + x2 = 0 + -4.346938776 Combine like terms: 4.346938776 + -4.346938776 = 0.000000000 0.000000000 + -4.346938776x + x2 = 0 + -4.346938776 -4.346938776x + x2 = 0 + -4.346938776 Combine like terms: 0 + -4.346938776 = -4.346938776 -4.346938776x + x2 = -4.346938776 The x term is -4.346938776x. Take half its coefficient (-2.173469388). Square it (4.723969181) and add it to both sides. Add '4.723969181' to each side of the equation. -4.346938776x + 4.723969181 + x2 = -4.346938776 + 4.723969181 Reorder the terms: 4.723969181 + -4.346938776x + x2 = -4.346938776 + 4.723969181 Combine like terms: -4.346938776 + 4.723969181 = 0.377030405 4.723969181 + -4.346938776x + x2 = 0.377030405 Factor a perfect square on the left side: (x + -2.173469388)(x + -2.173469388) = 0.377030405 Calculate the square root of the right side: 0.614028016 Break this problem into two subproblems by setting (x + -2.173469388) equal to 0.614028016 and -0.614028016.Subproblem 1
x + -2.173469388 = 0.614028016 Simplifying x + -2.173469388 = 0.614028016 Reorder the terms: -2.173469388 + x = 0.614028016 Solving -2.173469388 + x = 0.614028016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.173469388' to each side of the equation. -2.173469388 + 2.173469388 + x = 0.614028016 + 2.173469388 Combine like terms: -2.173469388 + 2.173469388 = 0.000000000 0.000000000 + x = 0.614028016 + 2.173469388 x = 0.614028016 + 2.173469388 Combine like terms: 0.614028016 + 2.173469388 = 2.787497404 x = 2.787497404 Simplifying x = 2.787497404Subproblem 2
x + -2.173469388 = -0.614028016 Simplifying x + -2.173469388 = -0.614028016 Reorder the terms: -2.173469388 + x = -0.614028016 Solving -2.173469388 + x = -0.614028016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.173469388' to each side of the equation. -2.173469388 + 2.173469388 + x = -0.614028016 + 2.173469388 Combine like terms: -2.173469388 + 2.173469388 = 0.000000000 0.000000000 + x = -0.614028016 + 2.173469388 x = -0.614028016 + 2.173469388 Combine like terms: -0.614028016 + 2.173469388 = 1.559441372 x = 1.559441372 Simplifying x = 1.559441372Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.787497404, 1.559441372}
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