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Simplifying 5(2x + 4) * 3x + -7 = 0 Reorder the terms: 5(4 + 2x) * 3x + -7 = 0 Reorder the terms for easier multiplication: 5 * 3x(4 + 2x) + -7 = 0 Multiply 5 * 3 15x(4 + 2x) + -7 = 0 (4 * 15x + 2x * 15x) + -7 = 0 (60x + 30x2) + -7 = 0 Reorder the terms: -7 + 60x + 30x2 = 0 Solving -7 + 60x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.2333333333 + 2x + x2 = 0.0 Move the constant term to the right: Add '0.2333333333' to each side of the equation. -0.2333333333 + 2x + 0.2333333333 + x2 = 0.0 + 0.2333333333 Reorder the terms: -0.2333333333 + 0.2333333333 + 2x + x2 = 0.0 + 0.2333333333 Combine like terms: -0.2333333333 + 0.2333333333 = 0.0000000000 0.0000000000 + 2x + x2 = 0.0 + 0.2333333333 2x + x2 = 0.0 + 0.2333333333 Combine like terms: 0.0 + 0.2333333333 = 0.2333333333 2x + x2 = 0.2333333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.2333333333 + 1 Reorder the terms: 1 + 2x + x2 = 0.2333333333 + 1 Combine like terms: 0.2333333333 + 1 = 1.2333333333 1 + 2x + x2 = 1.2333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.2333333333 Calculate the square root of the right side: 1.110555417 Break this problem into two subproblems by setting (x + 1) equal to 1.110555417 and -1.110555417.Subproblem 1
x + 1 = 1.110555417 Simplifying x + 1 = 1.110555417 Reorder the terms: 1 + x = 1.110555417 Solving 1 + x = 1.110555417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.110555417 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.110555417 + -1 x = 1.110555417 + -1 Combine like terms: 1.110555417 + -1 = 0.110555417 x = 0.110555417 Simplifying x = 0.110555417Subproblem 2
x + 1 = -1.110555417 Simplifying x + 1 = -1.110555417 Reorder the terms: 1 + x = -1.110555417 Solving 1 + x = -1.110555417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.110555417 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.110555417 + -1 x = -1.110555417 + -1 Combine like terms: -1.110555417 + -1 = -2.110555417 x = -2.110555417 Simplifying x = -2.110555417Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.110555417, -2.110555417}
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