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Simplifying 50 * 2 + -2x + -1x + -1x2 = 4x2 + 9 Multiply 50 * 2 100 + -2x + -1x + -1x2 = 4x2 + 9 Combine like terms: -2x + -1x = -3x 100 + -3x + -1x2 = 4x2 + 9 Reorder the terms: 100 + -3x + -1x2 = 9 + 4x2 Solving 100 + -3x + -1x2 = 9 + 4x2 Solving for variable 'x'. Reorder the terms: 100 + -9 + -3x + -1x2 + -4x2 = 9 + 4x2 + -9 + -4x2 Combine like terms: 100 + -9 = 91 91 + -3x + -1x2 + -4x2 = 9 + 4x2 + -9 + -4x2 Combine like terms: -1x2 + -4x2 = -5x2 91 + -3x + -5x2 = 9 + 4x2 + -9 + -4x2 Reorder the terms: 91 + -3x + -5x2 = 9 + -9 + 4x2 + -4x2 Combine like terms: 9 + -9 = 0 91 + -3x + -5x2 = 0 + 4x2 + -4x2 91 + -3x + -5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 91 + -3x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -18.2 + 0.6x + x2 = 0 Move the constant term to the right: Add '18.2' to each side of the equation. -18.2 + 0.6x + 18.2 + x2 = 0 + 18.2 Reorder the terms: -18.2 + 18.2 + 0.6x + x2 = 0 + 18.2 Combine like terms: -18.2 + 18.2 = 0.0 0.0 + 0.6x + x2 = 0 + 18.2 0.6x + x2 = 0 + 18.2 Combine like terms: 0 + 18.2 = 18.2 0.6x + x2 = 18.2 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 18.2 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 18.2 + 0.09 Combine like terms: 18.2 + 0.09 = 18.29 0.09 + 0.6x + x2 = 18.29 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 18.29 Calculate the square root of the right side: 4.276680956 Break this problem into two subproblems by setting (x + 0.3) equal to 4.276680956 and -4.276680956.Subproblem 1
x + 0.3 = 4.276680956 Simplifying x + 0.3 = 4.276680956 Reorder the terms: 0.3 + x = 4.276680956 Solving 0.3 + x = 4.276680956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 4.276680956 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 4.276680956 + -0.3 x = 4.276680956 + -0.3 Combine like terms: 4.276680956 + -0.3 = 3.976680956 x = 3.976680956 Simplifying x = 3.976680956Subproblem 2
x + 0.3 = -4.276680956 Simplifying x + 0.3 = -4.276680956 Reorder the terms: 0.3 + x = -4.276680956 Solving 0.3 + x = -4.276680956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -4.276680956 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -4.276680956 + -0.3 x = -4.276680956 + -0.3 Combine like terms: -4.276680956 + -0.3 = -4.576680956 x = -4.576680956 Simplifying x = -4.576680956Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.976680956, -4.576680956}
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