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Simplifying 419.8x + -7x2 = 11x + 2069.76 Reorder the terms: 419.8x + -7x2 = 2069.76 + 11x Solving 419.8x + -7x2 = 2069.76 + 11x Solving for variable 'x'. Reorder the terms: -2069.76 + 419.8x + -11x + -7x2 = 2069.76 + 11x + -2069.76 + -11x Combine like terms: 419.8x + -11x = 408.8x -2069.76 + 408.8x + -7x2 = 2069.76 + 11x + -2069.76 + -11x Reorder the terms: -2069.76 + 408.8x + -7x2 = 2069.76 + -2069.76 + 11x + -11x Combine like terms: 2069.76 + -2069.76 = 0.00 -2069.76 + 408.8x + -7x2 = 0.00 + 11x + -11x -2069.76 + 408.8x + -7x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -2069.76 + 408.8x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 295.68 + -58.4x + x2 = 0 Move the constant term to the right: Add '-295.68' to each side of the equation. 295.68 + -58.4x + -295.68 + x2 = 0 + -295.68 Reorder the terms: 295.68 + -295.68 + -58.4x + x2 = 0 + -295.68 Combine like terms: 295.68 + -295.68 = 0.00 0.00 + -58.4x + x2 = 0 + -295.68 -58.4x + x2 = 0 + -295.68 Combine like terms: 0 + -295.68 = -295.68 -58.4x + x2 = -295.68 The x term is -58.4x. Take half its coefficient (-29.2). Square it (852.64) and add it to both sides. Add '852.64' to each side of the equation. -58.4x + 852.64 + x2 = -295.68 + 852.64 Reorder the terms: 852.64 + -58.4x + x2 = -295.68 + 852.64 Combine like terms: -295.68 + 852.64 = 556.96 852.64 + -58.4x + x2 = 556.96 Factor a perfect square on the left side: (x + -29.2)(x + -29.2) = 556.96 Calculate the square root of the right side: 23.6 Break this problem into two subproblems by setting (x + -29.2) equal to 23.6 and -23.6.Subproblem 1
x + -29.2 = 23.6 Simplifying x + -29.2 = 23.6 Reorder the terms: -29.2 + x = 23.6 Solving -29.2 + x = 23.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.2' to each side of the equation. -29.2 + 29.2 + x = 23.6 + 29.2 Combine like terms: -29.2 + 29.2 = 0.0 0.0 + x = 23.6 + 29.2 x = 23.6 + 29.2 Combine like terms: 23.6 + 29.2 = 52.8 x = 52.8 Simplifying x = 52.8Subproblem 2
x + -29.2 = -23.6 Simplifying x + -29.2 = -23.6 Reorder the terms: -29.2 + x = -23.6 Solving -29.2 + x = -23.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.2' to each side of the equation. -29.2 + 29.2 + x = -23.6 + 29.2 Combine like terms: -29.2 + 29.2 = 0.0 0.0 + x = -23.6 + 29.2 x = -23.6 + 29.2 Combine like terms: -23.6 + 29.2 = 5.6 x = 5.6 Simplifying x = 5.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.8, 5.6}
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