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Simplifying 14x(10x + -3) = 17 Reorder the terms: 14x(-3 + 10x) = 17 (-3 * 14x + 10x * 14x) = 17 (-42x + 140x2) = 17 Solving -42x + 140x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + -42x + 140x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -42x + 140x2 = 0 Begin completing the square. Divide all terms by 140 the coefficient of the squared term: Divide each side by '140'. -0.1214285714 + -0.3x + x2 = 0.0 Move the constant term to the right: Add '0.1214285714' to each side of the equation. -0.1214285714 + -0.3x + 0.1214285714 + x2 = 0.0 + 0.1214285714 Reorder the terms: -0.1214285714 + 0.1214285714 + -0.3x + x2 = 0.0 + 0.1214285714 Combine like terms: -0.1214285714 + 0.1214285714 = 0.0000000000 0.0000000000 + -0.3x + x2 = 0.0 + 0.1214285714 -0.3x + x2 = 0.0 + 0.1214285714 Combine like terms: 0.0 + 0.1214285714 = 0.1214285714 -0.3x + x2 = 0.1214285714 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 0.1214285714 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 0.1214285714 + 0.0225 Combine like terms: 0.1214285714 + 0.0225 = 0.1439285714 0.0225 + -0.3x + x2 = 0.1439285714 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 0.1439285714 Calculate the square root of the right side: 0.379379192 Break this problem into two subproblems by setting (x + -0.15) equal to 0.379379192 and -0.379379192.Subproblem 1
x + -0.15 = 0.379379192 Simplifying x + -0.15 = 0.379379192 Reorder the terms: -0.15 + x = 0.379379192 Solving -0.15 + x = 0.379379192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 0.379379192 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.379379192 + 0.15 x = 0.379379192 + 0.15 Combine like terms: 0.379379192 + 0.15 = 0.529379192 x = 0.529379192 Simplifying x = 0.529379192Subproblem 2
x + -0.15 = -0.379379192 Simplifying x + -0.15 = -0.379379192 Reorder the terms: -0.15 + x = -0.379379192 Solving -0.15 + x = -0.379379192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -0.379379192 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.379379192 + 0.15 x = -0.379379192 + 0.15 Combine like terms: -0.379379192 + 0.15 = -0.229379192 x = -0.229379192 Simplifying x = -0.229379192Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.529379192, -0.229379192}
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