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Simplifying 3x + -40 + 7x * 5x + -20 + 4 = 40 + 5x * 2x + -8 Reorder the terms for easier multiplication: 3x + -40 + 7 * 5x * x + -20 + 4 = 40 + 5x * 2x + -8 Multiply 7 * 5 3x + -40 + 35x * x + -20 + 4 = 40 + 5x * 2x + -8 Multiply x * x 3x + -40 + 35x2 + -20 + 4 = 40 + 5x * 2x + -8 Reorder the terms: -40 + -20 + 4 + 3x + 35x2 = 40 + 5x * 2x + -8 Combine like terms: -40 + -20 = -60 -60 + 4 + 3x + 35x2 = 40 + 5x * 2x + -8 Combine like terms: -60 + 4 = -56 -56 + 3x + 35x2 = 40 + 5x * 2x + -8 Reorder the terms for easier multiplication: -56 + 3x + 35x2 = 40 + 5 * 2x * x + -8 Multiply 5 * 2 -56 + 3x + 35x2 = 40 + 10x * x + -8 Multiply x * x -56 + 3x + 35x2 = 40 + 10x2 + -8 Reorder the terms: -56 + 3x + 35x2 = 40 + -8 + 10x2 Combine like terms: 40 + -8 = 32 -56 + 3x + 35x2 = 32 + 10x2 Solving -56 + 3x + 35x2 = 32 + 10x2 Solving for variable 'x'. Reorder the terms: -56 + -32 + 3x + 35x2 + -10x2 = 32 + 10x2 + -32 + -10x2 Combine like terms: -56 + -32 = -88 -88 + 3x + 35x2 + -10x2 = 32 + 10x2 + -32 + -10x2 Combine like terms: 35x2 + -10x2 = 25x2 -88 + 3x + 25x2 = 32 + 10x2 + -32 + -10x2 Reorder the terms: -88 + 3x + 25x2 = 32 + -32 + 10x2 + -10x2 Combine like terms: 32 + -32 = 0 -88 + 3x + 25x2 = 0 + 10x2 + -10x2 -88 + 3x + 25x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -88 + 3x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -3.52 + 0.12x + x2 = 0 Move the constant term to the right: Add '3.52' to each side of the equation. -3.52 + 0.12x + 3.52 + x2 = 0 + 3.52 Reorder the terms: -3.52 + 3.52 + 0.12x + x2 = 0 + 3.52 Combine like terms: -3.52 + 3.52 = 0.00 0.00 + 0.12x + x2 = 0 + 3.52 0.12x + x2 = 0 + 3.52 Combine like terms: 0 + 3.52 = 3.52 0.12x + x2 = 3.52 The x term is 0.12x. Take half its coefficient (0.06). Square it (0.0036) and add it to both sides. Add '0.0036' to each side of the equation. 0.12x + 0.0036 + x2 = 3.52 + 0.0036 Reorder the terms: 0.0036 + 0.12x + x2 = 3.52 + 0.0036 Combine like terms: 3.52 + 0.0036 = 3.5236 0.0036 + 0.12x + x2 = 3.5236 Factor a perfect square on the left side: (x + 0.06)(x + 0.06) = 3.5236 Calculate the square root of the right side: 1.877125462 Break this problem into two subproblems by setting (x + 0.06) equal to 1.877125462 and -1.877125462.Subproblem 1
x + 0.06 = 1.877125462 Simplifying x + 0.06 = 1.877125462 Reorder the terms: 0.06 + x = 1.877125462 Solving 0.06 + x = 1.877125462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = 1.877125462 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = 1.877125462 + -0.06 x = 1.877125462 + -0.06 Combine like terms: 1.877125462 + -0.06 = 1.817125462 x = 1.817125462 Simplifying x = 1.817125462Subproblem 2
x + 0.06 = -1.877125462 Simplifying x + 0.06 = -1.877125462 Reorder the terms: 0.06 + x = -1.877125462 Solving 0.06 + x = -1.877125462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = -1.877125462 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = -1.877125462 + -0.06 x = -1.877125462 + -0.06 Combine like terms: -1.877125462 + -0.06 = -1.937125462 x = -1.937125462 Simplifying x = -1.937125462Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.817125462, -1.937125462}
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