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Simplifying 14x2 + 30x = 10 Reorder the terms: 30x + 14x2 = 10 Solving 30x + 14x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 30x + 14x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 30x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 15x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 15x + 7x2)' equal to zero and attempt to solve: Simplifying -5 + 15x + 7x2 = 0 Solving -5 + 15x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 2.142857143x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 2.142857143x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 2.142857143x + x2 = 0 + 0.7142857143 2.142857143x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 2.142857143x + x2 = 0.7142857143 The x term is 2.142857143x. Take half its coefficient (1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. 2.142857143x + 1.147959185 + x2 = 0.7142857143 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = 0.7142857143 + 1.147959185 Combine like terms: 0.7142857143 + 1.147959185 = 1.8622448993 1.147959185 + 2.142857143x + x2 = 1.8622448993 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = 1.8622448993 Calculate the square root of the right side: 1.364640942 Break this problem into two subproblems by setting (x + 1.071428572) equal to 1.364640942 and -1.364640942.Subproblem 1
x + 1.071428572 = 1.364640942 Simplifying x + 1.071428572 = 1.364640942 Reorder the terms: 1.071428572 + x = 1.364640942 Solving 1.071428572 + x = 1.364640942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = 1.364640942 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 1.364640942 + -1.071428572 x = 1.364640942 + -1.071428572 Combine like terms: 1.364640942 + -1.071428572 = 0.29321237 x = 0.29321237 Simplifying x = 0.29321237Subproblem 2
x + 1.071428572 = -1.364640942 Simplifying x + 1.071428572 = -1.364640942 Reorder the terms: 1.071428572 + x = -1.364640942 Solving 1.071428572 + x = -1.364640942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = -1.364640942 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -1.364640942 + -1.071428572 x = -1.364640942 + -1.071428572 Combine like terms: -1.364640942 + -1.071428572 = -2.436069514 x = -2.436069514 Simplifying x = -2.436069514Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.29321237, -2.436069514}Solution
x = {0.29321237, -2.436069514}
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