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Simplifying -4x + 100 = 5 + 0.1x2 Reorder the terms: 100 + -4x = 5 + 0.1x2 Solving 100 + -4x = 5 + 0.1x2 Solving for variable 'x'. Reorder the terms: 100 + -5 + -4x + -0.1x2 = 5 + 0.1x2 + -5 + -0.1x2 Combine like terms: 100 + -5 = 95 95 + -4x + -0.1x2 = 5 + 0.1x2 + -5 + -0.1x2 Reorder the terms: 95 + -4x + -0.1x2 = 5 + -5 + 0.1x2 + -0.1x2 Combine like terms: 5 + -5 = 0 95 + -4x + -0.1x2 = 0 + 0.1x2 + -0.1x2 95 + -4x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 95 + -4x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -950 + 40x + x2 = 0 Move the constant term to the right: Add '950' to each side of the equation. -950 + 40x + 950 + x2 = 0 + 950 Reorder the terms: -950 + 950 + 40x + x2 = 0 + 950 Combine like terms: -950 + 950 = 0 0 + 40x + x2 = 0 + 950 40x + x2 = 0 + 950 Combine like terms: 0 + 950 = 950 40x + x2 = 950 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 950 + 400 Reorder the terms: 400 + 40x + x2 = 950 + 400 Combine like terms: 950 + 400 = 1350 400 + 40x + x2 = 1350 Factor a perfect square on the left side: (x + 20)(x + 20) = 1350 Calculate the square root of the right side: 36.742346142 Break this problem into two subproblems by setting (x + 20) equal to 36.742346142 and -36.742346142.Subproblem 1
x + 20 = 36.742346142 Simplifying x + 20 = 36.742346142 Reorder the terms: 20 + x = 36.742346142 Solving 20 + x = 36.742346142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 36.742346142 + -20 Combine like terms: 20 + -20 = 0 0 + x = 36.742346142 + -20 x = 36.742346142 + -20 Combine like terms: 36.742346142 + -20 = 16.742346142 x = 16.742346142 Simplifying x = 16.742346142Subproblem 2
x + 20 = -36.742346142 Simplifying x + 20 = -36.742346142 Reorder the terms: 20 + x = -36.742346142 Solving 20 + x = -36.742346142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -36.742346142 + -20 Combine like terms: 20 + -20 = 0 0 + x = -36.742346142 + -20 x = -36.742346142 + -20 Combine like terms: -36.742346142 + -20 = -56.742346142 x = -56.742346142 Simplifying x = -56.742346142Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.742346142, -56.742346142}
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