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Simplifying 10x(3x + 4) + 10 = 4x Reorder the terms: 10x(4 + 3x) + 10 = 4x (4 * 10x + 3x * 10x) + 10 = 4x (40x + 30x2) + 10 = 4x Reorder the terms: 10 + 40x + 30x2 = 4x Solving 10 + 40x + 30x2 = 4x Solving for variable 'x'. Reorder the terms: 10 + 40x + -4x + 30x2 = 4x + -4x Combine like terms: 40x + -4x = 36x 10 + 36x + 30x2 = 4x + -4x Combine like terms: 4x + -4x = 0 10 + 36x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 18x + 15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 18x + 15x2)' equal to zero and attempt to solve: Simplifying 5 + 18x + 15x2 = 0 Solving 5 + 18x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.3333333333 + 1.2x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 1.2x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 1.2x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 1.2x + x2 = 0 + -0.3333333333 1.2x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 1.2x + x2 = -0.3333333333 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = -0.3333333333 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = -0.3333333333 + 0.36 Combine like terms: -0.3333333333 + 0.36 = 0.0266666667 0.36 + 1.2x + x2 = 0.0266666667 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.0266666667 Calculate the square root of the right side: 0.163299316 Break this problem into two subproblems by setting (x + 0.6) equal to 0.163299316 and -0.163299316.Subproblem 1
x + 0.6 = 0.163299316 Simplifying x + 0.6 = 0.163299316 Reorder the terms: 0.6 + x = 0.163299316 Solving 0.6 + x = 0.163299316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 0.163299316 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.163299316 + -0.6 x = 0.163299316 + -0.6 Combine like terms: 0.163299316 + -0.6 = -0.436700684 x = -0.436700684 Simplifying x = -0.436700684Subproblem 2
x + 0.6 = -0.163299316 Simplifying x + 0.6 = -0.163299316 Reorder the terms: 0.6 + x = -0.163299316 Solving 0.6 + x = -0.163299316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -0.163299316 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.163299316 + -0.6 x = -0.163299316 + -0.6 Combine like terms: -0.163299316 + -0.6 = -0.763299316 x = -0.763299316 Simplifying x = -0.763299316Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.436700684, -0.763299316}Solution
x = {-0.436700684, -0.763299316}
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