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Simplifying 3 = 7x(10x + 4) Reorder the terms: 3 = 7x(4 + 10x) 3 = (4 * 7x + 10x * 7x) 3 = (28x + 70x2) Solving 3 = 28x + 70x2 Solving for variable 'x'. Reorder the terms: 3 + -28x + -70x2 = 28x + -28x + 70x2 + -70x2 Combine like terms: 28x + -28x = 0 3 + -28x + -70x2 = 0 + 70x2 + -70x2 3 + -28x + -70x2 = 70x2 + -70x2 Combine like terms: 70x2 + -70x2 = 0 3 + -28x + -70x2 = 0 Begin completing the square. Divide all terms by -70 the coefficient of the squared term: Divide each side by '-70'. -0.04285714286 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.04285714286' to each side of the equation. -0.04285714286 + 0.4x + 0.04285714286 + x2 = 0 + 0.04285714286 Reorder the terms: -0.04285714286 + 0.04285714286 + 0.4x + x2 = 0 + 0.04285714286 Combine like terms: -0.04285714286 + 0.04285714286 = 0.00000000000 0.00000000000 + 0.4x + x2 = 0 + 0.04285714286 0.4x + x2 = 0 + 0.04285714286 Combine like terms: 0 + 0.04285714286 = 0.04285714286 0.4x + x2 = 0.04285714286 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.04285714286 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.04285714286 + 0.04 Combine like terms: 0.04285714286 + 0.04 = 0.08285714286 0.04 + 0.4x + x2 = 0.08285714286 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.08285714286 Calculate the square root of the right side: 0.287849167 Break this problem into two subproblems by setting (x + 0.2) equal to 0.287849167 and -0.287849167.Subproblem 1
x + 0.2 = 0.287849167 Simplifying x + 0.2 = 0.287849167 Reorder the terms: 0.2 + x = 0.287849167 Solving 0.2 + x = 0.287849167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.287849167 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.287849167 + -0.2 x = 0.287849167 + -0.2 Combine like terms: 0.287849167 + -0.2 = 0.087849167 x = 0.087849167 Simplifying x = 0.087849167Subproblem 2
x + 0.2 = -0.287849167 Simplifying x + 0.2 = -0.287849167 Reorder the terms: 0.2 + x = -0.287849167 Solving 0.2 + x = -0.287849167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.287849167 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.287849167 + -0.2 x = -0.287849167 + -0.2 Combine like terms: -0.287849167 + -0.2 = -0.487849167 x = -0.487849167 Simplifying x = -0.487849167Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.087849167, -0.487849167}
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