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Simplifying (0.3 + 2x)(0.7 + 2x) = 7.12 Multiply (0.3 + 2x) * (0.7 + 2x) (0.3(0.7 + 2x) + 2x * (0.7 + 2x)) = 7.12 ((0.7 * 0.3 + 2x * 0.3) + 2x * (0.7 + 2x)) = 7.12 ((0.21 + 0.6x) + 2x * (0.7 + 2x)) = 7.12 (0.21 + 0.6x + (0.7 * 2x + 2x * 2x)) = 7.12 (0.21 + 0.6x + (1.4x + 4x2)) = 7.12 Combine like terms: 0.6x + 1.4x = 2x (0.21 + 2x + 4x2) = 7.12 Solving 0.21 + 2x + 4x2 = 7.12 Solving for variable 'x'. Reorder the terms: 0.21 + -7.12 + 2x + 4x2 = 7.12 + -7.12 Combine like terms: 0.21 + -7.12 = -6.91 -6.91 + 2x + 4x2 = 7.12 + -7.12 Combine like terms: 7.12 + -7.12 = 0.00 -6.91 + 2x + 4x2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.7275 + 0.5x + x2 = 0.00 Move the constant term to the right: Add '1.7275' to each side of the equation. -1.7275 + 0.5x + 1.7275 + x2 = 0.00 + 1.7275 Reorder the terms: -1.7275 + 1.7275 + 0.5x + x2 = 0.00 + 1.7275 Combine like terms: -1.7275 + 1.7275 = 0.0000 0.0000 + 0.5x + x2 = 0.00 + 1.7275 0.5x + x2 = 0.00 + 1.7275 Combine like terms: 0.00 + 1.7275 = 1.7275 0.5x + x2 = 1.7275 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1.7275 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.7275 + 0.0625 Combine like terms: 1.7275 + 0.0625 = 1.79 0.0625 + 0.5x + x2 = 1.79 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.79 Calculate the square root of the right side: 1.337908816 Break this problem into two subproblems by setting (x + 0.25) equal to 1.337908816 and -1.337908816.Subproblem 1
x + 0.25 = 1.337908816 Simplifying x + 0.25 = 1.337908816 Reorder the terms: 0.25 + x = 1.337908816 Solving 0.25 + x = 1.337908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.337908816 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.337908816 + -0.25 x = 1.337908816 + -0.25 Combine like terms: 1.337908816 + -0.25 = 1.087908816 x = 1.087908816 Simplifying x = 1.087908816Subproblem 2
x + 0.25 = -1.337908816 Simplifying x + 0.25 = -1.337908816 Reorder the terms: 0.25 + x = -1.337908816 Solving 0.25 + x = -1.337908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.337908816 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.337908816 + -0.25 x = -1.337908816 + -0.25 Combine like terms: -1.337908816 + -0.25 = -1.587908816 x = -1.587908816 Simplifying x = -1.587908816Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.087908816, -1.587908816}
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