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Simplifying 7x(5x + 4) = 6 Reorder the terms: 7x(4 + 5x) = 6 (4 * 7x + 5x * 7x) = 6 (28x + 35x2) = 6 Solving 28x + 35x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 28x + 35x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 28x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.1714285714 + 0.8x + x2 = 0 Move the constant term to the right: Add '0.1714285714' to each side of the equation. -0.1714285714 + 0.8x + 0.1714285714 + x2 = 0 + 0.1714285714 Reorder the terms: -0.1714285714 + 0.1714285714 + 0.8x + x2 = 0 + 0.1714285714 Combine like terms: -0.1714285714 + 0.1714285714 = 0.0000000000 0.0000000000 + 0.8x + x2 = 0 + 0.1714285714 0.8x + x2 = 0 + 0.1714285714 Combine like terms: 0 + 0.1714285714 = 0.1714285714 0.8x + x2 = 0.1714285714 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 0.1714285714 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 0.1714285714 + 0.16 Combine like terms: 0.1714285714 + 0.16 = 0.3314285714 0.16 + 0.8x + x2 = 0.3314285714 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 0.3314285714 Calculate the square root of the right side: 0.575698334 Break this problem into two subproblems by setting (x + 0.4) equal to 0.575698334 and -0.575698334.Subproblem 1
x + 0.4 = 0.575698334 Simplifying x + 0.4 = 0.575698334 Reorder the terms: 0.4 + x = 0.575698334 Solving 0.4 + x = 0.575698334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 0.575698334 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.575698334 + -0.4 x = 0.575698334 + -0.4 Combine like terms: 0.575698334 + -0.4 = 0.175698334 x = 0.175698334 Simplifying x = 0.175698334Subproblem 2
x + 0.4 = -0.575698334 Simplifying x + 0.4 = -0.575698334 Reorder the terms: 0.4 + x = -0.575698334 Solving 0.4 + x = -0.575698334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -0.575698334 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.575698334 + -0.4 x = -0.575698334 + -0.4 Combine like terms: -0.575698334 + -0.4 = -0.975698334 x = -0.975698334 Simplifying x = -0.975698334Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.175698334, -0.975698334}
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