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Simplifying (0.3 + 2x)(0.6 + 2x) = 6.02598 Multiply (0.3 + 2x) * (0.6 + 2x) (0.3(0.6 + 2x) + 2x * (0.6 + 2x)) = 6.02598 ((0.6 * 0.3 + 2x * 0.3) + 2x * (0.6 + 2x)) = 6.02598 ((0.18 + 0.6x) + 2x * (0.6 + 2x)) = 6.02598 (0.18 + 0.6x + (0.6 * 2x + 2x * 2x)) = 6.02598 (0.18 + 0.6x + (1.2x + 4x2)) = 6.02598 Combine like terms: 0.6x + 1.2x = 1.8x (0.18 + 1.8x + 4x2) = 6.02598 Solving 0.18 + 1.8x + 4x2 = 6.02598 Solving for variable 'x'. Reorder the terms: 0.18 + -6.02598 + 1.8x + 4x2 = 6.02598 + -6.02598 Combine like terms: 0.18 + -6.02598 = -5.84598 -5.84598 + 1.8x + 4x2 = 6.02598 + -6.02598 Combine like terms: 6.02598 + -6.02598 = 0.00000 -5.84598 + 1.8x + 4x2 = 0.00000 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.461495 + 0.45x + x2 = 0.00000 Move the constant term to the right: Add '1.461495' to each side of the equation. -1.461495 + 0.45x + 1.461495 + x2 = 0.00000 + 1.461495 Reorder the terms: -1.461495 + 1.461495 + 0.45x + x2 = 0.00000 + 1.461495 Combine like terms: -1.461495 + 1.461495 = 0.000000 0.000000 + 0.45x + x2 = 0.00000 + 1.461495 0.45x + x2 = 0.00000 + 1.461495 Combine like terms: 0.00000 + 1.461495 = 1.461495 0.45x + x2 = 1.461495 The x term is 0.45x. Take half its coefficient (0.225). Square it (0.050625) and add it to both sides. Add '0.050625' to each side of the equation. 0.45x + 0.050625 + x2 = 1.461495 + 0.050625 Reorder the terms: 0.050625 + 0.45x + x2 = 1.461495 + 0.050625 Combine like terms: 1.461495 + 0.050625 = 1.51212 0.050625 + 0.45x + x2 = 1.51212 Factor a perfect square on the left side: (x + 0.225)(x + 0.225) = 1.51212 Calculate the square root of the right side: 1.229682886 Break this problem into two subproblems by setting (x + 0.225) equal to 1.229682886 and -1.229682886.Subproblem 1
x + 0.225 = 1.229682886 Simplifying x + 0.225 = 1.229682886 Reorder the terms: 0.225 + x = 1.229682886 Solving 0.225 + x = 1.229682886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.225' to each side of the equation. 0.225 + -0.225 + x = 1.229682886 + -0.225 Combine like terms: 0.225 + -0.225 = 0.000 0.000 + x = 1.229682886 + -0.225 x = 1.229682886 + -0.225 Combine like terms: 1.229682886 + -0.225 = 1.004682886 x = 1.004682886 Simplifying x = 1.004682886Subproblem 2
x + 0.225 = -1.229682886 Simplifying x + 0.225 = -1.229682886 Reorder the terms: 0.225 + x = -1.229682886 Solving 0.225 + x = -1.229682886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.225' to each side of the equation. 0.225 + -0.225 + x = -1.229682886 + -0.225 Combine like terms: 0.225 + -0.225 = 0.000 0.000 + x = -1.229682886 + -0.225 x = -1.229682886 + -0.225 Combine like terms: -1.229682886 + -0.225 = -1.454682886 x = -1.454682886 Simplifying x = -1.454682886Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.004682886, -1.454682886}
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